generate random string for div id

I want to display YouTube videos on my website, but I need to be able to add a unique id for each video that's going to be shared by users. So I put this together, and I have run into a little problem. I am trying to get the JavaScript to add a random string for the div id, but it's not working, showing the string:

<script type='text/javascript' src='jwplayer.js'></script>
<script type='text/javascript'>
function randomString(length) {
    var chars = '0123456789ABCDEFGHIJKLMNOPQRSTUVWXTZabcdefghiklmnopqrstuvwxyz'.split('');

    if (! length) {
        length = Math.floor(Math.random() * chars.length);
    }

    var str = '';
    for (var i = 0; i < length; i++) {
        str += chars[Math.floor(Math.random() * chars.length)];
    }
    return str;
}

var div = randomString(8);
</script>

<div id='div()'>This text will be replaced</div>

<script type='text/javascript'>
  jwplayer('div()').setup({
    'flashplayer': 'player.swf',
    'file': 'http://www.youtube.com/watch?v=4AX0bi9GXXY',
    'controlbar': 'bottom',
    'width': '470',
    'height': '320'
  });
</script>

I really like this function:

function guidGenerator() {
    var S4 = function() {
       return (((1+Math.random())*0x10000)|0).toString(16).substring(1);
    };
    return (S4()+S4()+"-"+S4()+"-"+S4()+"-"+S4()+"-"+S4()+S4()+S4());
}

From Create GUID / UUID in JavaScript?


2018 edit: I think this answer has some interesting info, but for any practical applications you should use Joe's answer instead.

A simple way to create a unique ID in JavaScript is to use the Date object:

var uniqid = Date.now();

That gives you the total milliseconds elapsed since January 1st 1970, which is a unique value every time you call that.

The problem with that value now is that you cannot use it as an element's ID, since in HTML, IDs need to start with an alphabetical character. There is also the problem that two users doing an action at the exact same time might result in the same ID. We could lessen the probability of that, and fix our alphabetical character problem, by appending a random letter before the numerical part of the ID.

var randLetter = String.fromCharCode(65 + Math.floor(Math.random() * 26));
var uniqid = randLetter + Date.now();

This still has a chance, however slim, of colliding though. Your best bet for a unique id is to keep a running count, increment it every time, and do all that in a single place, ie, on the server.