How do I check if file exists in jQuery or pure JavaScript?

A similar and more up-to-date approach.

$.get(url)
    .done(function() { 
        // exists code 
    }).fail(function() { 
        // not exists code
    })

With jQuery:

$.ajax({
    url:'http://www.example.com/somefile.ext',
    type:'HEAD',
    error: function()
    {
        //file not exists
    },
    success: function()
    {
        //file exists
    }
});

EDIT:

Here is the code for checking 404 status, without using jQuery

function UrlExists(url)
{
    var http = new XMLHttpRequest();
    http.open('HEAD', url, false);
    http.send();
    return http.status!=404;
}

Small changes and it could check for status HTTP status code 200 (success), instead.

EDIT 2: Since sync XMLHttpRequest is deprecated, you can add a utility method like this to do it async:

function executeIfFileExist(src, callback) {
    var xhr = new XMLHttpRequest()
    xhr.onreadystatechange = function() {
        if (this.readyState === this.DONE) {
            callback()
        }
    }
    xhr.open('HEAD', src)
}