Compared to other URL shortening sites, bit.ly is fairly new on the scene, although I'm sure you've seen it in use on Twitter lately.
What's cool about bit.ly is the fact that it will place a cookie on your browser and remember the last 15 links you've shortened. You can also track the amount of traffic you're getting from your shortened links, and it gives you the ability to create a custom URL ending to your link.
bit.ly can post your shortened URL to your Twitter page as well — just make sure you log in.
Suffice to say, bit.ly is one hot shortening site.