It would be so awesome if I had some demo applications I could download and play with!
Lucky for you, there are a bunch of demo apps that you can grab and dig through. You’ll find them on the Wiki at http://wiki.developers.facebook.com/index.php/Demos. The current crop of three demos includes:
An extremely basic application included with the PHP 4 and PHP 5 clients. You can play with a live demo at http://apps.facebook.com/footprints/.
A more advanced demo showing some of the more complex features, including Mock Ajax, FBJS, and the Data Store API. It’s backed by premade data on your MySQL server and/or the Facebook Data Store API.
Another “real” application, demonstrating building applications that are installable both for users and for Facebook Pages, such as those for businesses, bands, and brands.
In addition to the apps provided by Facebook, Jesse Stay (author of O’Reilly’s excellent FBML Essentials and coauthor of I’m on Facebook—Now What???) has built an app that demonstrates almost all of the FBML tags; see http://apps.facebook.com/fbmlessentials.