I'm not sure an online company would be able to do it.
You would have to make the click go through them and have them forward the surfer to your page. It wouldn't work like a page counter where they can just put a 1 pixel graphic on your site and count how many times it was loaded. If you are willing to "link through" them then there are probably places that will do it.
Anyone know if TinyUrl gives click stats? That would be one way to do it.
That's what I think, but I've been wrong MANY times before.
Did you try searching on google? I just got over 1 million results for "free click tracking". A lot of them looked to be selling scripts like the one I mentioned, but if you look through the list you might find what you need.