Following on from what Alex has said, here's only a few features on Facebook where chances are it uses Ajax:
- The three icons at the top-left to alert you of any new friend requests, private messages, or notifications
- The search box
- The news feed (regularly updates itself)
- Recommended pages (when you like/dismiss one, it'll show another)
- Shows which friends are online
- Facebook chat itself
- The news feed again when you scroll to the bottom
And the list above only shows the ones that are fully automated on the
Home page!! These will be fetched regularly from a database by using a JavaScript timer. I'm not even going to mention the ones where you click to activate an Ajax script, simply because there's far too many! If you click on a link anywhere on Facebook, 98% of the time it will run an Ajax script one way or another. Notice that when you go to another page, the http address doesn't really change, but only the end part after a hash (#), pretty much like for a bookmark anchor... yep, you guessed it, the entire clean-up of a page and loading a new one is done through Ajax as well! That's why the top and bottom bar stays where they are; even after what seems to be like going to a new page as it shows completely different content, you are still in fact on the same page.