I need list of all class name of Font-Awesome

April 2017 edit: Updated to 4.7.0

As linked in the comments on your question, Font Awesome provides a Cheatsheet page which lists all icon previews, class names and character codes and even lists aliases (fa-automobile, for instance, which is an alias of fa-car).

• 4.*.* Cheatsheet: http://fortawesome.github.io/Font-Awesome/cheatsheet
• 3.2.1 Cheatsheet: http://fortawesome.github.io/Font-Awesome/3.2.1/cheatsheet

There are a total of 593 icon class names (including aliases) in version 4.3.0. Here is the list in the format you desire (including aliases, but with no " (alias)" comments):

["fa-500px", "fa-address-book", "fa-address-book-o", "fa-address-card", "fa-address-card-o", "fa-adjust", "fa-adn", "fa-align-center", "fa-align-justify", "fa-align-left", "fa-align-right", "fa-amazon", "fa-ambulance", "fa-american-sign-language-interpreting", "fa-anchor", "fa-android", "fa-angellist", "fa-angle-double-down", "fa-angle-double-left", "fa-angle-double-right", "fa-angle-double-up", "fa-angle-down", "fa-angle-left", "fa-angle-right", "fa-angle-up", "fa-apple", "fa-archive", "fa-area-chart", "fa-arrow-circle-down", "fa-arrow-circle-left", "fa-arrow-circle-o-down", "fa-arrow-circle-o-left", "fa-arrow-circle-o-right", "fa-arrow-circle-o-up", "fa-arrow-circle-right", "fa-arrow-circle-up", "fa-arrow-down", "fa-arrow-left", "fa-arrow-right", "fa-arrow-up", "fa-arrows", "fa-arrows-alt", "fa-arrows-h", "fa-arrows-v", "fa-asl-interpreting", "fa-assistive-listening-systems", "fa-asterisk", "fa-at", "fa-audio-description", "fa-automobile", "fa-backward", "fa-balance-scale", "fa-ban", "fa-bandcamp", "fa-bank", "fa-bar-chart", "fa-bar-chart-o", "fa-barcode", "fa-bars", "fa-bath", "fa-bathtub", "fa-battery", "fa-battery-0", "fa-battery-1", "fa-battery-2", "fa-battery-3", "fa-battery-4", "fa-battery-empty", "fa-battery-full", "fa-battery-half", "fa-battery-quarter", "fa-battery-three-quarters", "fa-bed", "fa-beer", "fa-behance", "fa-behance-square", "fa-bell", "fa-bell-o", "fa-bell-slash", "fa-bell-slash-o", "fa-bicycle", "fa-binoculars", "fa-birthday-cake", "fa-bitbucket", "fa-bitbucket-square", "fa-bitcoin", "fa-black-tie", "fa-blind", "fa-bluetooth", "fa-bluetooth-b", "fa-bold", "fa-bolt", "fa-bomb", "fa-book", "fa-bookmark", "fa-bookmark-o", "fa-braille", "fa-briefcase", "fa-btc", "fa-bug", "fa-building", "fa-building-o", "fa-bullhorn", "fa-bullseye", "fa-bus", "fa-buysellads", "fa-cab", "fa-calculator", "fa-calendar", "fa-calendar-check-o", "fa-calendar-minus-o", "fa-calendar-o", "fa-calendar-plus-o", "fa-calendar-times-o", "fa-camera", "fa-camera-retro", "fa-car", "fa-caret-down", "fa-caret-left", "fa-caret-right", "fa-caret-square-o-down", "fa-caret-square-o-left", "fa-caret-square-o-right", "fa-caret-square-o-up", "fa-caret-up", "fa-cart-arrow-down", "fa-cart-plus", "fa-cc", "fa-cc-amex", "fa-cc-diners-club", "fa-cc-discover", "fa-cc-jcb", "fa-cc-mastercard", "fa-cc-paypal", "fa-cc-stripe", "fa-cc-visa", "fa-certificate", "fa-chain", "fa-chain-broken", "fa-check", "fa-check-circle", "fa-check-circle-o", "fa-check-square", "fa-check-square-o", "fa-chevron-circle-down", "fa-chevron-circle-left", "fa-chevron-circle-right", "fa-chevron-circle-up", "fa-chevron-down", "fa-chevron-left", "fa-chevron-right", "fa-chevron-up", "fa-child", "fa-chrome", "fa-circle", "fa-circle-o", "fa-circle-o-notch", "fa-circle-thin", "fa-clipboard", "fa-clock-o", "fa-clone", "fa-close", "fa-cloud", "fa-cloud-download", "fa-cloud-upload", "fa-cny", "fa-code", "fa-code-fork", "fa-codepen", "fa-codiepie", "fa-coffee", "fa-cog", "fa-cogs", "fa-columns", "fa-comment", "fa-comment-o", "fa-commenting", "fa-commenting-o", "fa-comments", "fa-comments-o", "fa-compass", "fa-compress", "fa-connectdevelop", "fa-contao", "fa-copy", "fa-copyright", "fa-creative-commons", "fa-credit-card", "fa-credit-card-alt", "fa-crop", "fa-crosshairs", "fa-css3", "fa-cube", "fa-cubes", "fa-cut", "fa-cutlery", "fa-dashboard", "fa-dashcube", "fa-database", "fa-deaf", "fa-deafness", "fa-dedent", "fa-delicious", "fa-desktop", "fa-deviantart", "fa-diamond", "fa-digg", "fa-dollar", "fa-dot-circle-o", "fa-download", "fa-dribbble", "fa-drivers-license", "fa-drivers-license-o", "fa-dropbox", "fa-drupal", "fa-edge", "fa-edit", "fa-eercast", "fa-eject", "fa-ellipsis-h", "fa-ellipsis-v", "fa-empire", "fa-envelope", "fa-envelope-o", "fa-envelope-open", "fa-envelope-open-o", "fa-envelope-square", "fa-envira", "fa-eraser", "fa-etsy", "fa-eur", "fa-euro", "fa-exchange", "fa-exclamation", "fa-exclamation-circle", "fa-exclamation-triangle", "fa-expand", "fa-expeditedssl", "fa-external-link", "fa-external-link-square", "fa-eye", "fa-eye-slash", "fa-eyedropper", "fa-fa", "fa-facebook", "fa-facebook-f", "fa-facebook-official", "fa-facebook-square", "fa-fast-backward", "fa-fast-forward", "fa-fax", "fa-feed", "fa-female", "fa-fighter-jet", "fa-file", "fa-file-archive-o", "fa-file-audio-o", "fa-file-code-o", "fa-file-excel-o", "fa-file-image-o", "fa-file-movie-o", "fa-file-o", "fa-file-pdf-o", "fa-file-photo-o", "fa-file-picture-o", "fa-file-powerpoint-o", "fa-file-sound-o", "fa-file-text", "fa-file-text-o", "fa-file-video-o", "fa-file-word-o", "fa-file-zip-o", "fa-files-o", "fa-film", "fa-filter", "fa-fire", "fa-fire-extinguisher", "fa-firefox", "fa-first-order", "fa-flag", "fa-flag-checkered", "fa-flag-o", "fa-flash", "fa-flask", "fa-flickr", "fa-floppy-o", "fa-folder", "fa-folder-o", "fa-folder-open", "fa-folder-open-o", "fa-font", "fa-font-awesome", "fa-fonticons", "fa-fort-awesome", "fa-forumbee", "fa-forward", "fa-foursquare", "fa-free-code-camp", "fa-frown-o", "fa-futbol-o", "fa-gamepad", "fa-gavel", "fa-gbp", "fa-ge", "fa-gear", "fa-gears", "fa-genderless", "fa-get-pocket", "fa-gg", "fa-gg-circle", "fa-gift", "fa-git", "fa-git-square", "fa-github", "fa-github-alt", "fa-github-square", "fa-gitlab", "fa-gittip", "fa-glass", "fa-glide", "fa-glide-g", "fa-globe", "fa-google", "fa-google-plus", "fa-google-plus-circle", "fa-google-plus-official", "fa-google-plus-square", "fa-google-wallet", "fa-graduation-cap", "fa-gratipay", "fa-grav", "fa-group", "fa-h-square", "fa-hacker-news", "fa-hand-grab-o", "fa-hand-lizard-o", "fa-hand-o-down", "fa-hand-o-left", "fa-hand-o-right", "fa-hand-o-up", "fa-hand-paper-o", "fa-hand-peace-o", "fa-hand-pointer-o", "fa-hand-rock-o", "fa-hand-scissors-o", "fa-hand-spock-o", "fa-hand-stop-o", "fa-handshake-o", "fa-hard-of-hearing", "fa-hashtag", "fa-hdd-o", "fa-header", "fa-headphones", "fa-heart", "fa-heart-o", "fa-heartbeat", "fa-history", "fa-home", "fa-hospital-o", "fa-hotel", "fa-hourglass", "fa-hourglass-1", "fa-hourglass-2", "fa-hourglass-3", "fa-hourglass-end", "fa-hourglass-half", "fa-hourglass-o", "fa-hourglass-start", "fa-houzz", "fa-html5", "fa-i-cursor", "fa-id-badge", "fa-id-card", "fa-id-card-o", "fa-ils", "fa-image", "fa-imdb", "fa-inbox", "fa-indent", "fa-industry", "fa-info", "fa-info-circle", "fa-inr", "fa-instagram", "fa-institution", "fa-internet-explorer", "fa-intersex", "fa-ioxhost", "fa-italic", "fa-joomla", "fa-jpy", "fa-jsfiddle", "fa-key", "fa-keyboard-o", "fa-krw", "fa-language", "fa-laptop", "fa-lastfm", "fa-lastfm-square", "fa-leaf", "fa-leanpub", "fa-legal", "fa-lemon-o", "fa-level-down", "fa-level-up", "fa-life-bouy", "fa-life-buoy", "fa-life-ring", "fa-life-saver", "fa-lightbulb-o", "fa-line-chart", "fa-link", "fa-linkedin", "fa-linkedin-square", "fa-linode", "fa-linux", "fa-list", "fa-list-alt", "fa-list-ol", "fa-list-ul", "fa-location-arrow", "fa-lock", "fa-long-arrow-down", "fa-long-arrow-left", "fa-long-arrow-right", "fa-long-arrow-up", "fa-low-vision", "fa-magic", "fa-magnet", "fa-mail-forward", "fa-mail-reply", "fa-mail-reply-all", "fa-male", "fa-map", "fa-map-marker", "fa-map-o", "fa-map-pin", "fa-map-signs", "fa-mars", "fa-mars-double", "fa-mars-stroke", "fa-mars-stroke-h", "fa-mars-stroke-v", "fa-maxcdn", "fa-meanpath", "fa-medium", "fa-medkit", "fa-meetup", "fa-meh-o", "fa-mercury", "fa-microchip", "fa-microphone", "fa-microphone-slash", "fa-minus", "fa-minus-circle", "fa-minus-square", "fa-minus-square-o", "fa-mixcloud", "fa-mobile", "fa-mobile-phone", "fa-modx", "fa-money", "fa-moon-o", "fa-mortar-board", "fa-motorcycle", "fa-mouse-pointer", "fa-music", "fa-navicon", "fa-neuter", "fa-newspaper-o", "fa-object-group", "fa-object-ungroup", "fa-odnoklassniki", "fa-odnoklassniki-square", "fa-opencart", "fa-openid", "fa-opera", "fa-optin-monster", "fa-outdent", "fa-pagelines", "fa-paint-brush", "fa-paper-plane", "fa-paper-plane-o", "fa-paperclip", "fa-paragraph", "fa-paste", "fa-pause", "fa-pause-circle", "fa-pause-circle-o", "fa-paw", "fa-paypal", "fa-pencil", "fa-pencil-square", "fa-pencil-square-o", "fa-percent", "fa-phone", "fa-phone-square", "fa-photo", "fa-picture-o", "fa-pie-chart", "fa-pied-piper", "fa-pied-piper-alt", "fa-pied-piper-pp", "fa-pinterest", "fa-pinterest-p", "fa-pinterest-square", "fa-plane", "fa-play", "fa-play-circle", "fa-play-circle-o", "fa-plug", "fa-plus", "fa-plus-circle", "fa-plus-square", "fa-plus-square-o", "fa-podcast", "fa-power-off", "fa-print", "fa-product-hunt", "fa-puzzle-piece", "fa-qq", "fa-qrcode", "fa-question", "fa-question-circle", "fa-question-circle-o", "fa-quora", "fa-quote-left", "fa-quote-right", "fa-ra", "fa-random", "fa-ravelry", "fa-rebel", "fa-recycle", "fa-reddit", "fa-reddit-alien", "fa-reddit-square", "fa-refresh", "fa-registered", "fa-remove", "fa-renren", "fa-reorder", "fa-repeat", "fa-reply", "fa-reply-all", "fa-resistance", "fa-retweet", "fa-rmb", "fa-road", "fa-rocket", "fa-rotate-left", "fa-rotate-right", "fa-rouble", "fa-rss", "fa-rss-square", "fa-rub", "fa-ruble", "fa-rupee", "fa-s15", "fa-safari", "fa-save", "fa-scissors", "fa-scribd", "fa-search", "fa-search-minus", "fa-search-plus", "fa-sellsy", "fa-send", "fa-send-o", "fa-server", "fa-share", "fa-share-alt", "fa-share-alt-square", "fa-share-square", "fa-share-square-o", "fa-shekel", "fa-sheqel", "fa-shield", "fa-ship", "fa-shirtsinbulk", "fa-shopping-bag", "fa-shopping-basket", "fa-shopping-cart", "fa-shower", "fa-sign-in", "fa-sign-language", "fa-sign-out", "fa-signal", "fa-signing", "fa-simplybuilt", "fa-sitemap", "fa-skyatlas", "fa-skype", "fa-slack", "fa-sliders", "fa-slideshare", "fa-smile-o", "fa-snapchat", "fa-snapchat-ghost", "fa-snapchat-square", "fa-snowflake-o", "fa-soccer-ball-o", "fa-sort", "fa-sort-alpha-asc", "fa-sort-alpha-desc", "fa-sort-amount-asc", "fa-sort-amount-desc", "fa-sort-asc", "fa-sort-desc", "fa-sort-down", "fa-sort-numeric-asc", "fa-sort-numeric-desc", "fa-sort-up", "fa-soundcloud", "fa-space-shuttle", "fa-spinner", "fa-spoon", "fa-spotify", "fa-square", "fa-square-o", "fa-stack-exchange", "fa-stack-overflow", "fa-star", "fa-star-half", "fa-star-half-empty", "fa-star-half-full", "fa-star-half-o", "fa-star-o", "fa-steam", "fa-steam-square", "fa-step-backward", "fa-step-forward", "fa-stethoscope", "fa-sticky-note", "fa-sticky-note-o", "fa-stop", "fa-stop-circle", "fa-stop-circle-o", "fa-street-view", "fa-strikethrough", "fa-stumbleupon", "fa-stumbleupon-circle", "fa-subscript", "fa-subway", "fa-suitcase", "fa-sun-o", "fa-superpowers", "fa-superscript", "fa-support", "fa-table", "fa-tablet", "fa-tachometer", "fa-tag", "fa-tags", "fa-tasks", "fa-taxi", "fa-telegram", "fa-television", "fa-tencent-weibo", "fa-terminal", "fa-text-height", "fa-text-width", "fa-th", "fa-th-large", "fa-th-list", "fa-themeisle", "fa-thermometer", "fa-thermometer-0", "fa-thermometer-1", "fa-thermometer-2", "fa-thermometer-3", "fa-thermometer-4", "fa-thermometer-empty", "fa-thermometer-full", "fa-thermometer-half", "fa-thermometer-quarter", "fa-thermometer-three-quarters", "fa-thumb-tack", "fa-thumbs-down", "fa-thumbs-o-down", "fa-thumbs-o-up", "fa-thumbs-up", "fa-ticket", "fa-times", "fa-times-circle", "fa-times-circle-o", "fa-times-rectangle", "fa-times-rectangle-o", "fa-tint", "fa-toggle-down", "fa-toggle-left", "fa-toggle-off", "fa-toggle-on", "fa-toggle-right", "fa-toggle-up", "fa-trademark", "fa-train", "fa-transgender", "fa-transgender-alt", "fa-trash", "fa-trash-o", "fa-tree", "fa-trello", "fa-tripadvisor", "fa-trophy", "fa-truck", "fa-try", "fa-tty", "fa-tumblr", "fa-tumblr-square", "fa-turkish-lira", "fa-tv", "fa-twitch", "fa-twitter", "fa-twitter-square", "fa-umbrella", "fa-underline", "fa-undo", "fa-universal-access", "fa-university", "fa-unlink", "fa-unlock", "fa-unlock-alt", "fa-unsorted", "fa-upload", "fa-usb", "fa-usd", "fa-user", "fa-user-circle", "fa-user-circle-o", "fa-user-md", "fa-user-o", "fa-user-plus", "fa-user-secret", "fa-user-times", "fa-users", "fa-vcard", "fa-vcard-o", "fa-venus", "fa-venus-double", "fa-venus-mars", "fa-viacoin", "fa-viadeo", "fa-viadeo-square", "fa-video-camera", "fa-vimeo", "fa-vimeo-square", "fa-vine", "fa-vk", "fa-volume-control-phone", "fa-volume-down", "fa-volume-off", "fa-volume-up", "fa-warning", "fa-wechat", "fa-weibo", "fa-weixin", "fa-whatsapp", "fa-wheelchair", "fa-wheelchair-alt", "fa-wifi", "fa-wikipedia-w", "fa-window-close", "fa-window-close-o", "fa-window-maximize", "fa-window-minimize", "fa-window-restore", "fa-windows", "fa-won", "fa-wordpress", "fa-wpbeginner", "fa-wpexplorer", "fa-wpforms", "fa-wrench", "fa-xing", "fa-xing-square", "fa-y-combinator", "fa-y-combinator-square", "fa-yahoo", "fa-yc", "fa-yc-square", "fa-yelp", "fa-yen", "fa-yoast", "fa-youtube", "fa-youtube-play", "fa-youtube-square"]

And here is the full list of version 4.3 icon class names, including aliases, as a list:

fa-500px
fa-address-book
fa-address-book-o
fa-address-card
fa-address-card-o
fa-adjust
fa-adn
fa-align-center
fa-align-justify
fa-align-left
fa-align-right
fa-amazon
fa-ambulance
fa-american-sign-language-interpreting
fa-anchor
fa-android
fa-angellist
fa-angle-double-down
fa-angle-double-left
fa-angle-double-right
fa-angle-double-up
fa-angle-down
fa-angle-left
fa-angle-right
fa-angle-up
fa-apple
fa-archive
fa-area-chart
fa-arrow-circle-down
fa-arrow-circle-left
fa-arrow-circle-o-down
fa-arrow-circle-o-left
fa-arrow-circle-o-right
fa-arrow-circle-o-up
fa-arrow-circle-right
fa-arrow-circle-up
fa-arrow-down
fa-arrow-left
fa-arrow-right
fa-arrow-up
fa-arrows
fa-arrows-alt
fa-arrows-h
fa-arrows-v
fa-asl-interpreting
fa-assistive-listening-systems
fa-asterisk
fa-at
fa-audio-description
fa-automobile
fa-backward
fa-balance-scale
fa-ban
fa-bandcamp
fa-bank
fa-bar-chart
fa-bar-chart-o
fa-barcode
fa-bars
fa-bath
fa-bathtub
fa-battery
fa-battery-0
fa-battery-1
fa-battery-2
fa-battery-3
fa-battery-4
fa-battery-empty
fa-battery-full
fa-battery-half
fa-battery-quarter
fa-battery-three-quarters
fa-bed
fa-beer
fa-behance
fa-behance-square
fa-bell
fa-bell-o
fa-bell-slash
fa-bell-slash-o
fa-bicycle
fa-binoculars
fa-birthday-cake
fa-bitbucket
fa-bitbucket-square
fa-bitcoin
fa-black-tie
fa-blind
fa-bluetooth
fa-bluetooth-b
fa-bold
fa-bolt
fa-bomb
fa-book
fa-bookmark
fa-bookmark-o
fa-braille
fa-briefcase
fa-btc
fa-bug
fa-building
fa-building-o
fa-bullhorn
fa-bullseye
fa-bus
fa-buysellads
fa-cab
fa-calculator
fa-calendar
fa-calendar-check-o
fa-calendar-minus-o
fa-calendar-o
fa-calendar-plus-o
fa-calendar-times-o
fa-camera
fa-camera-retro
fa-car
fa-caret-down
fa-caret-left
fa-caret-right
fa-caret-square-o-down
fa-caret-square-o-left
fa-caret-square-o-right
fa-caret-square-o-up
fa-caret-up
fa-cart-arrow-down
fa-cart-plus
fa-cc
fa-cc-amex
fa-cc-diners-club
fa-cc-discover
fa-cc-jcb
fa-cc-mastercard
fa-cc-paypal
fa-cc-stripe
fa-cc-visa
fa-certificate
fa-chain
fa-chain-broken
fa-check
fa-check-circle
fa-check-circle-o
fa-check-square
fa-check-square-o
fa-chevron-circle-down
fa-chevron-circle-left
fa-chevron-circle-right
fa-chevron-circle-up
fa-chevron-down
fa-chevron-left
fa-chevron-right
fa-chevron-up
fa-child
fa-chrome
fa-circle
fa-circle-o
fa-circle-o-notch
fa-circle-thin
fa-clipboard
fa-clock-o
fa-clone
fa-close
fa-cloud
fa-cloud-download
fa-cloud-upload
fa-cny
fa-code
fa-code-fork
fa-codepen
fa-codiepie
fa-coffee
fa-cog
fa-cogs
fa-columns
fa-comment
fa-comment-o
fa-commenting
fa-commenting-o
fa-comments
fa-comments-o
fa-compass
fa-compress
fa-connectdevelop
fa-contao
fa-copy
fa-copyright
fa-creative-commons
fa-credit-card
fa-credit-card-alt
fa-crop
fa-crosshairs
fa-css3
fa-cube
fa-cubes
fa-cut
fa-cutlery
fa-dashboard
fa-dashcube
fa-database
fa-deaf
fa-deafness
fa-dedent
fa-delicious
fa-desktop
fa-deviantart
fa-diamond
fa-digg
fa-dollar
fa-dot-circle-o
fa-download
fa-dribbble
fa-drivers-license
fa-drivers-license-o
fa-dropbox
fa-drupal
fa-edge
fa-edit
fa-eercast
fa-eject
fa-ellipsis-h
fa-ellipsis-v
fa-empire
fa-envelope
fa-envelope-o
fa-envelope-open
fa-envelope-open-o
fa-envelope-square
fa-envira
fa-eraser
fa-etsy
fa-eur
fa-euro
fa-exchange
fa-exclamation
fa-exclamation-circle
fa-exclamation-triangle
fa-expand
fa-expeditedssl
fa-external-link
fa-external-link-square
fa-eye
fa-eye-slash
fa-eyedropper
fa-fa
fa-facebook
fa-facebook-f
fa-facebook-official
fa-facebook-square
fa-fast-backward
fa-fast-forward
fa-fax
fa-feed
fa-female
fa-fighter-jet
fa-file
fa-file-archive-o
fa-file-audio-o
fa-file-code-o
fa-file-excel-o
fa-file-image-o
fa-file-movie-o
fa-file-o
fa-file-pdf-o
fa-file-photo-o
fa-file-picture-o
fa-file-powerpoint-o
fa-file-sound-o
fa-file-text
fa-file-text-o
fa-file-video-o
fa-file-word-o
fa-file-zip-o
fa-files-o
fa-film
fa-filter
fa-fire
fa-fire-extinguisher
fa-firefox
fa-first-order
fa-flag
fa-flag-checkered
fa-flag-o
fa-flash
fa-flask
fa-flickr
fa-floppy-o
fa-folder
fa-folder-o
fa-folder-open
fa-folder-open-o
fa-font
fa-font-awesome
fa-fonticons
fa-fort-awesome
fa-forumbee
fa-forward
fa-foursquare
fa-free-code-camp
fa-frown-o
fa-futbol-o
fa-gamepad
fa-gavel
fa-gbp
fa-ge
fa-gear
fa-gears
fa-genderless
fa-get-pocket
fa-gg
fa-gg-circle
fa-gift
fa-git
fa-git-square
fa-github
fa-github-alt
fa-github-square
fa-gitlab
fa-gittip
fa-glass
fa-glide
fa-glide-g
fa-globe
fa-google
fa-google-plus
fa-google-plus-circle
fa-google-plus-official
fa-google-plus-square
fa-google-wallet
fa-graduation-cap
fa-gratipay
fa-grav
fa-group
fa-h-square
fa-hacker-news
fa-hand-grab-o
fa-hand-lizard-o
fa-hand-o-down
fa-hand-o-left
fa-hand-o-right
fa-hand-o-up
fa-hand-paper-o
fa-hand-peace-o
fa-hand-pointer-o
fa-hand-rock-o
fa-hand-scissors-o
fa-hand-spock-o
fa-hand-stop-o
fa-handshake-o
fa-hard-of-hearing
fa-hashtag
fa-hdd-o
fa-header
fa-headphones
fa-heart
fa-heart-o
fa-heartbeat
fa-history
fa-home
fa-hospital-o
fa-hotel
fa-hourglass
fa-hourglass-1
fa-hourglass-2
fa-hourglass-3
fa-hourglass-end
fa-hourglass-half
fa-hourglass-o
fa-hourglass-start
fa-houzz
fa-html5
fa-i-cursor
fa-id-badge
fa-id-card
fa-id-card-o
fa-ils
fa-image
fa-imdb
fa-inbox
fa-indent
fa-industry
fa-info
fa-info-circle
fa-inr
fa-instagram
fa-institution
fa-internet-explorer
fa-intersex
fa-ioxhost
fa-italic
fa-joomla
fa-jpy
fa-jsfiddle
fa-key
fa-keyboard-o
fa-krw
fa-language
fa-laptop
fa-lastfm
fa-lastfm-square
fa-leaf
fa-leanpub
fa-legal
fa-lemon-o
fa-level-down
fa-level-up
fa-life-bouy
fa-life-buoy
fa-life-ring
fa-life-saver
fa-lightbulb-o
fa-line-chart
fa-link
fa-linkedin
fa-linkedin-square
fa-linode
fa-linux
fa-list
fa-list-alt
fa-list-ol
fa-list-ul
fa-location-arrow
fa-lock
fa-long-arrow-down
fa-long-arrow-left
fa-long-arrow-right
fa-long-arrow-up
fa-low-vision
fa-magic
fa-magnet
fa-mail-forward
fa-mail-reply
fa-mail-reply-all
fa-male
fa-map
fa-map-marker
fa-map-o
fa-map-pin
fa-map-signs
fa-mars
fa-mars-double
fa-mars-stroke
fa-mars-stroke-h
fa-mars-stroke-v
fa-maxcdn
fa-meanpath
fa-medium
fa-medkit
fa-meetup
fa-meh-o
fa-mercury
fa-microchip
fa-microphone
fa-microphone-slash
fa-minus
fa-minus-circle
fa-minus-square
fa-minus-square-o
fa-mixcloud
fa-mobile
fa-mobile-phone
fa-modx
fa-money
fa-moon-o
fa-mortar-board
fa-motorcycle
fa-mouse-pointer
fa-music
fa-navicon
fa-neuter
fa-newspaper-o
fa-object-group
fa-object-ungroup
fa-odnoklassniki
fa-odnoklassniki-square
fa-opencart
fa-openid
fa-opera
fa-optin-monster
fa-outdent
fa-pagelines
fa-paint-brush
fa-paper-plane
fa-paper-plane-o
fa-paperclip
fa-paragraph
fa-paste
fa-pause
fa-pause-circle
fa-pause-circle-o
fa-paw
fa-paypal
fa-pencil
fa-pencil-square
fa-pencil-square-o
fa-percent
fa-phone
fa-phone-square
fa-photo
fa-picture-o
fa-pie-chart
fa-pied-piper
fa-pied-piper-alt
fa-pied-piper-pp
fa-pinterest
fa-pinterest-p
fa-pinterest-square
fa-plane
fa-play
fa-play-circle
fa-play-circle-o
fa-plug
fa-plus
fa-plus-circle
fa-plus-square
fa-plus-square-o
fa-podcast
fa-power-off
fa-print
fa-product-hunt
fa-puzzle-piece
fa-qq
fa-qrcode
fa-question
fa-question-circle
fa-question-circle-o
fa-quora
fa-quote-left
fa-quote-right
fa-ra
fa-random
fa-ravelry
fa-rebel
fa-recycle
fa-reddit
fa-reddit-alien
fa-reddit-square
fa-refresh
fa-registered
fa-remove
fa-renren
fa-reorder
fa-repeat
fa-reply
fa-reply-all
fa-resistance
fa-retweet
fa-rmb
fa-road
fa-rocket
fa-rotate-left
fa-rotate-right
fa-rouble
fa-rss
fa-rss-square
fa-rub
fa-ruble
fa-rupee
fa-s15
fa-safari
fa-save
fa-scissors
fa-scribd
fa-search
fa-search-minus
fa-search-plus
fa-sellsy
fa-send
fa-send-o
fa-server
fa-share
fa-share-alt
fa-share-alt-square
fa-share-square
fa-share-square-o
fa-shekel
fa-sheqel
fa-shield
fa-ship
fa-shirtsinbulk
fa-shopping-bag
fa-shopping-basket
fa-shopping-cart
fa-shower
fa-sign-in
fa-sign-language
fa-sign-out
fa-signal
fa-signing
fa-simplybuilt
fa-sitemap
fa-skyatlas
fa-skype
fa-slack
fa-sliders
fa-slideshare
fa-smile-o
fa-snapchat
fa-snapchat-ghost
fa-snapchat-square
fa-snowflake-o
fa-soccer-ball-o
fa-sort
fa-sort-alpha-asc
fa-sort-alpha-desc
fa-sort-amount-asc
fa-sort-amount-desc
fa-sort-asc
fa-sort-desc
fa-sort-down
fa-sort-numeric-asc
fa-sort-numeric-desc
fa-sort-up
fa-soundcloud
fa-space-shuttle
fa-spinner
fa-spoon
fa-spotify
fa-square
fa-square-o
fa-stack-exchange
fa-stack-overflow
fa-star
fa-star-half
fa-star-half-empty
fa-star-half-full
fa-star-half-o
fa-star-o
fa-steam
fa-steam-square
fa-step-backward
fa-step-forward
fa-stethoscope
fa-sticky-note
fa-sticky-note-o
fa-stop
fa-stop-circle
fa-stop-circle-o
fa-street-view
fa-strikethrough
fa-stumbleupon
fa-stumbleupon-circle
fa-subscript
fa-subway
fa-suitcase
fa-sun-o
fa-superpowers
fa-superscript
fa-support
fa-table
fa-tablet
fa-tachometer
fa-tag
fa-tags
fa-tasks
fa-taxi
fa-telegram
fa-television
fa-tencent-weibo
fa-terminal
fa-text-height
fa-text-width
fa-th
fa-th-large
fa-th-list
fa-themeisle
fa-thermometer
fa-thermometer-0
fa-thermometer-1
fa-thermometer-2
fa-thermometer-3
fa-thermometer-4
fa-thermometer-empty
fa-thermometer-full
fa-thermometer-half
fa-thermometer-quarter
fa-thermometer-three-quarters
fa-thumb-tack
fa-thumbs-down
fa-thumbs-o-down
fa-thumbs-o-up
fa-thumbs-up
fa-ticket
fa-times
fa-times-circle
fa-times-circle-o
fa-times-rectangle
fa-times-rectangle-o
fa-tint
fa-toggle-down
fa-toggle-left
fa-toggle-off
fa-toggle-on
fa-toggle-right
fa-toggle-up
fa-trademark
fa-train
fa-transgender
fa-transgender-alt
fa-trash
fa-trash-o
fa-tree
fa-trello
fa-tripadvisor
fa-trophy
fa-truck
fa-try
fa-tty
fa-tumblr
fa-tumblr-square
fa-turkish-lira
fa-tv
fa-twitch
fa-twitter
fa-twitter-square
fa-umbrella
fa-underline
fa-undo
fa-universal-access
fa-university
fa-unlink
fa-unlock
fa-unlock-alt
fa-unsorted
fa-upload
fa-usb
fa-usd
fa-user
fa-user-circle
fa-user-circle-o
fa-user-md
fa-user-o
fa-user-plus
fa-user-secret
fa-user-times
fa-users
fa-vcard
fa-vcard-o
fa-venus
fa-venus-double
fa-venus-mars
fa-viacoin
fa-viadeo
fa-viadeo-square
fa-video-camera
fa-vimeo
fa-vimeo-square
fa-vine
fa-vk
fa-volume-control-phone
fa-volume-down
fa-volume-off
fa-volume-up
fa-warning
fa-wechat
fa-weibo
fa-weixin
fa-whatsapp
fa-wheelchair
fa-wheelchair-alt
fa-wifi
fa-wikipedia-w
fa-window-close
fa-window-close-o
fa-window-maximize
fa-window-minimize
fa-window-restore
fa-windows
fa-won
fa-wordpress
fa-wpbeginner
fa-wpexplorer
fa-wpforms
fa-wrench
fa-xing
fa-xing-square
fa-y-combinator
fa-y-combinator-square
fa-yahoo
fa-yc
fa-yc-square
fa-yelp
fa-yen
fa-yoast
fa-youtube
fa-youtube-play
fa-youtube-square

Another little script for posterity.

Update 02/2018 (version 5.x)

Latest working version, based on edit from Blasius Secondus (thanks).

Open the fonts cheat sheet and run the following snippet in the developper console: https://fontawesome.com/cheatsheet

var names = new Set();
var icons = document.getElementsByClassName('icon');
for (const icon of icons) {
  const name = icon.getElementsByTagName('dd')[0].innerText;
  names.add(name);
}
console.log(JSON.stringify(Array.from(names)));

If you want them sorted by section (solid/regular/brand):

var groups = {};
var sections = document.getElementsByClassName('cheatsheet-set');
for (const section of sections) {
  const names = [];
  groups[section.id] = names;
  var icons = section.getElementsByClassName('icon');
  for (const icon of icons) {
    const name = icon.getElementsByTagName('dd')[0].innerText;
    names.push(name);
  }
}
console.log(groups); // Feel free to stringify/manipulate

---

Original answer

Simply open the latest cheatsheet: http://fortawesome.github.io/Font-Awesome/cheatsheet/

Then in your browser, open the developer console and run:

var names = [];
$('.row .col-md-4').each(function() {
  var s = $(this).text();
  var m = s.match(/fa-.*/);
  if (m && m[0] && s.indexOf('(alias)') < 0) {
    names.push(m[0]);
  }
});
console.log( JSON.stringify( names ) );

If you want the list instead of an array, replace the last line by

console.log( names.join(' ') );

(You can use any separator you want instead of space ' ')

The advantage of this method is that you will only get the visual icons (not the fa-spin and friends), and not the duplicate aliases.