I have created a Firefox extension that submits the tracks you play at www.Pandora.com to Last.fm.
I liked Gabe's solution, but the first thought in my head was "do I really want to enter my password on a third-party site?", I know that others felt the same way, so I started working on a way to send the track data without any information ever reaching a third-party server.
Everything sent by this extension goes directly to the Last.fm servers and nowhere else.
It supports caching of the track data if the AudioScrobbler submission server is down or having issues.
It works in Firefox and Flock, and can probably be made to work in other Gecko browsers.
The code is Javascript and XUL, and uses XMLHttpRequest to send the data to the Audioscrobbler servers.
If you do decide to give it a try, please direct feature requests, and report any issues you have here.
Setup: After you install it and restart Firefox, click on the Tools menu and you will see a LastFM > item, select it and three more items will appear, click on LastFM Options to configure the extension.
Current version: 0.6.4.3.1 -- File updated: March 22, 2008, 08:41:10 GMT.