Google URL Shortener (goo.gl) was introduced in Dec'09 as part of Google Toolbar and Feedburner. Google've now launched it as a full web service; "We don't intend to overload goo.gl with features, but we do want it to be the stablest, most secure, and fastest URL shortener on the web. With goo.gl, every time you shorten a URL, you know it'll work fast, and when you click a goo.gl shortened URL, you're protected against malware, phishing and spam," said Google.
"If you sign-into your Google Account, you'll see a list of URLs you've shortened in past. Click "details" link next to any of shortened URL and you'll find public, real-time analytics data, complete with traffic over time, top referrers, and visitor profiles.
Also Google plan to release an official API for goo.gl in the future. You'll be able to use API to shorten URLs, expand URLs, and view analytics from directly within your own apps."
You can also use goo.gl URL Shortener, Shareaholic for Google Chrome and Firfox.
Bonus: Matt Cutts' tweeted, if you add ".qr" to the end of any goo.gl URL, it'll create a QR code. Scanning this with any QR code reader will take you to URL. So, for e.g., this URL: goo.gl/3BaI, is the shortened link for this post. If I make it: goo.gl/3BaI.qr, I'll get the image below:
More Info: Goo.gl