YOURLS (stands for Your Own URL Shortener) is a set of PHP scripts that allow you to create your own URL shortening service. Like most scripts its requirements Apache with Mod_Rewrite, PHP and MySQL which makes it easy to install in virtually any hosting account.
YOURLS allows you to automatically generate URLs as well as assign a short name yourself, which I found to be quite handy for URLs I use often. Other features include:
It has a simple web interface that lists all the short URLs created, the original URLs, how many times each URL was used as well other details. Opening an URL's information shows a lot of detailed statistics about it like traffic location and direct vs. referrer traffic.