There are many popular URL Shortening services provider on the web like tinyurl, bit.ly, su.pr, the basic idea for an URL shortening service is to replace the long URL in to easy to remember short URL, nowadays URL shortener websites demands are increasing in regular computer users in Social Networking Sites
PHPurl

PHPurl is a simple script to shorten URLs. Optionally, custom URLs can be defined for more readable links. The script is created with PHP & MySQL.
KISSA BE (updated)

kissa.be is shortener your url, email text and image and open source url shortener clone of tinyurl. below all features in the new latest version3.
1. Custom Url
2. Membership & twitter integration.
3. Copy 2 Clipboard
4. Statistic Page, Frame to iFrame.
5. Multilanguage support
6. Bookmarklet
7. Firefox add-on
8. Easy Installer Script
TightURL

TightURL is a PHP/MySQL script that has a nice spam control feature. It checks entries in various spam databases before shortening them.
phurl

The script has a captcha & re-captcha support to prevent bots. It also comes with a basic admin interface that enables deleting URLs.
YOURLS (Favorite)

YOURLS is a small set of PHP scripts that will allow you to run your own URL shortening service, you can pick custom keyword URLs, it comes with its own API. You will love it.