Google Blog about the short url service.

http://googleblog.blogspot.com/2009/12/making-urls-shorter-for-google-toolbar.html

Google short links a url short feature

Google also has a url short feature you can find that link here.

http://goo.gl/
All goo.gl URLs and click analytics are public and can be shared by anyone.

Google URL shortener

The Google URL Shortener at goo.gl is a service that takes long URLs and squeezes them into fewer characters to make a link easier to share, tweet, or email to friends. For example, the short URLhttp://goo.gl/l6MS is a convenient shorthand representation for the long URLhttp://googleblog.blogspot.com/2009/12/making-urls-shorter-for-google-toolbar.html.

After reading this article, if you still have questions about the Google URL Shortener and want to learn more, or would like to give us your feedback, see the Google URL shortener discussion group.

How do I use the Google URL Shortener?

Go to goo.gl and paste the long URL you wish to shorten into the input box at the top of the page. Click "Shorten" and to the right of the box you’ll see a short goo.gl URL that can be copied and pasted anywhere you’d like to share it.
If you’d like to track the analytics of your shortened URL, please sign in to your Google Account before shortening your URL. Your shortened URL will automatically be added to your goo.gl history.

Why use the Google URL Shortener?

People share a lot of links online. This is particularly true as microblogging services such as Twitter andGoogle Buzz have grown in popularity. With character limits in tweets, status updates, and other modes of short form publishing, a shorter URL leaves more room to say what's on your mind.
Our primary goal in making this service publicly available to all users is to harness Google’s global production infrastructure to provide users with the following benefits:

• Stability - reliable service with good uptime
• Security - warning message if the short URL points to a suspected malware, phishing, or spam website
• Speed - fast resolution of short URLs (in a few milliseconds)

List of many short URL services

Short URL Services

This link has a great list and features for alot of short url services.
http://www.toprankblog.com/2009/01/11-best-url-shortening-services-vote-your-favorite/

Short URL Service

Short URL Service