I'm a little late to the game, but until recently, there hasn't been much need for URL Shorteners. With Twitter and to a lesser extent, Facebook, sharing short links are a necessity. URL Shorteners provide a simple function: shrink a long URL that you can use in your post, tweet, status update or web articles. It is easy and handy to use a shortened URL once you find the right tool.
There are a handful that get regular use, like bit.ly and Tiny URL. You can do a search for "URL Shorteners" in your favorite search engine and find dozens more to choose from, all with different strengths and weaknesses. There are several different factors to be aware of, such as time to redirect, uptime and tracking statistics, but for me, the biggest factor is URL length. That is why I have been using, and highly recommend, u.nu.
I am sure as the market for URL Shorteners matures, there will be only a few that rise to the top, but as far as I can tell, demand is still growing and a clear-cut choice has not emerged. So until a market leader emerges and you are looking for the shortest URLs you can get, U.nu is should be on your short list.