Facebook has a shortener which is http://fb.me/ or http://on.fb.me/.
The URL is simply a shortener for http://www.facebook.com/, it does not otherwise give you an interface to create new URLs. Instead, you can use it to shorten the normal URL.
For instance, my account which is http://www.facebook.com/alexis.wilke can be shortened to: http://fb.me/alexis.wilke.
Note that going to http://fb.me/ sends you to your Facebook home page, just like http://www.facebook.com/ does.