Checking if a URL is broken in Javascript

I'd recommend to use jQuery for correct cross-browser ajax requests:

function UrlExists(url, cb){
    jQuery.ajax({
        url:      url,
        dataType: 'text',
        type:     'GET',
        complete:  function(xhr){
            if(typeof cb === 'function')
               cb.apply(this, [xhr.status]);
        }
    });
}

Usage:

UrlExists('/path/script.pl', function(status){
    if(status === 200){
       // file was found
    }
    else if(status === 404){
       // 404 not found
    }
});

Modern, cross and short way

checkLink = async url => (await fetch(url)).ok

which is same of:

async checkLink(url) { return (await fetch(url)).ok }

which is same of:

async function checkLink(url) { return (await fetch(url)).ok }

which is same of:

Note: Starting with Gecko 30.0 (Firefox 30.0 / Thunderbird 30.0 / SeaMonkey 2.27), Blink 39.0, and Edge 13, synchronous requests on the main thread have been deprecated due to their negative impact on the user experience.

Cross solution (old, deprecated)

function UrlExists(url) {
 var http = new XMLHttpRequest();
 http.open('HEAD', url, false);
 http.send();
 return http.status==200;
}