Globally override key binding in Emacs

Install use-package, eval and you're done:

(require 'bind-key)
(bind-key* "C-i" 'some-function)

I use a minor mode for all my "override" key bindings:

(defvar my-keys-minor-mode-map
  (let ((map (make-sparse-keymap)))
    (define-key map (kbd "C-i") 'some-function)
    map)
  "my-keys-minor-mode keymap.")

(define-minor-mode my-keys-minor-mode
  "A minor mode so that my key settings override annoying major modes."
  :init-value t
  :lighter " my-keys")

(my-keys-minor-mode 1)

This has the added benefit of being able to turn off all my modifications in one fell swoop (just disable the minor mode) in case someone else is driving the keyboard or if I need to see what a default key binding does.

Note that you may need to turn this off in the minibuffer:

(defun my-minibuffer-setup-hook ()
  (my-keys-minor-mode 0))

(add-hook 'minibuffer-setup-hook 'my-minibuffer-setup-hook)

As an addition to scottfrazer's answer, I've written the following so that my keybindings retain precedence, even if subsequently-loaded libraries bring in new keymaps of their own.

Because keymaps can be generated at compile time, load seemed like the best place to do this.

(add-hook 'after-load-functions 'my-keys-have-priority)

(defun my-keys-have-priority (_file)
  "Try to ensure that my keybindings retain priority over other minor modes.

Called via the `after-load-functions' special hook."
  (unless (eq (caar minor-mode-map-alist) 'my-keys-minor-mode)
    (let ((mykeys (assq 'my-keys-minor-mode minor-mode-map-alist)))
      (assq-delete-all 'my-keys-minor-mode minor-mode-map-alist)
      (add-to-list 'minor-mode-map-alist mykeys))))

I found this question while searching for "emacs undefine org mode keybindings", because I wanted to unbind the existing C-c C-b behavior to allow my global map to bury-buffer to work in an org buffer.

This ended up being the simplest solution for me:

(add-hook 'org-mode-hook
      (lambda ()
        (local-unset-key (kbd "C-c C-b"))))