The popularity of Twitter and similar microblogging and social messaging platforms has led to a new type of service on the Internet: the URL shortener. Because Twitter allows only 140 characters per tweet, it is important to conserve as much space as possible. URL shorteners help with this goal by taking a longform URL like http://webtrends.about.com/b/2008/11/14/14-fun-websites-and-web-activities.htm and shortening it to something that looks more like http://bit.ly/1a7YzQ. That's a net savings of 57 characters, which is over a third of a tweet.
The two important rules to remember are (1) only use an URL shortener when you need one and (2) only use URL shorteners with 301 redirects.
When to use an URL shortener. While URL shorteners are a great service for websites like Twitter, they should not be used when linking from articles or blog entries. When you don't need to conserve space, go with the longer form. A few years from now, the URL shortener may not work, but the longer form will.
Only use URL shortners with 301 redirects. A 301 redirect tells Google that the page has permanently moved. This is important because Google uses links to rank web pages. The more links, the higher up on the search page results the web page will appear, which translates to more traffic.
A list of URL shorteners with 301 redirects