I've been looking around for a really simple API that would be a nice place to get started using web services from PHP - and I realised that bit.ly actually fits the bill really well. They have straightforward api docs on google code, and it's also a pretty simple function!

Her code is about three lines consisting of a curl_init call to the bit.ly server with the URL, a curl_setopt to tell it to return the information and a curl_exec to execute. The result is a JSON string easily decoded with a "url" parameter containing the newly minted short URL. She also briefly mentions some of the other features of the bit.ly API including reverse translation and bundling of links.