I usually wait for a collection of asynchronous events to finish using a setInterval poller. Is there a better way?

Question

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Multiple ajax calls inside a each() function.. then do something once ALL of them are finished?

Consider the following function:

function suggestSong(songs){
    console.log("Suggesting song from songs:", songs);
    var self = this;
    var totalRelatedVideos = [];
    var count = 0;

    $.each(songs, function(){
        count++;
        self.getRelatedVideos(this.videoId, function(relatedVideos){
            count--;
            totalRelatedVideos = totalRelatedVideos.concat(relatedVideos);
        });
    });

    var maxWaitTime = 1000; 
    var waitTime = 200;
    var elapsedTime = 0;
    var waitInterval = setInterval(function(){
        elapsedTime += waitTime;
        if(count == 0 || elapsedTime >= maxWaitTime){
            clearInterval(waitInterval);
            console.log("I found related videos: " + totalRelatedVideos.length);
        }
    }, waitTime );
};

This is how I currently implement waiting for a collection of asynchronous events to finish before executing another piece of code. There's a lot of code to do very little, though. I was wondering if there's a less obtuse way of achieving the same result?