Google had its own URL shortener too. Earlier, the 'goo.gl' URL shortener was just integrated in Google services. Now, it has gone public. Google says that their service offers more stability, security and speed. Well, then it's one service to check out.
Also, there's an interesting aspect to this service. Unlike most others, Goo.gl can track your short links too. Now, here's what that means. The link I have in the previous paragraph has been shortened by Goo.gl. When I browse to the site now, I can see the number of clicks done on them. That's useful. So now you can see how many people have clicked your link and when.
So, go to Goo.gl now and start shortening your links.