I've been using TinyURL (www.tinyurl.com) for many years to generated short versions of longer URLs. One of the things I've liked most about TinyURL is that I can specify part of the URL, which allows me to use something both short and meaningful.
http://goo.gl/, instead. It does not let me customize the URL at all, which I miss a little bit, but since it is tied into my Google ID, it gives me nice features like analytics (e.g., link use counts, demographics, etc), a "home page" listing all of the shortened URLs I have created recently, and very short URLs.
But one word of caution: the links and analytics are world-readable, so do not use the Google URL trimmer if you have anything you want to keep semi-private.