Used it for various things. We have sessions that time out after a defined length of time (15 mins by default). We do however have AJAX keep the session active if the user is working.
It's useful for auto-saving too. Generally I use it for things that would still work if you took it back out.
One really cool thing I've implemented it in is exception handling in JavaScript. Sometimes you get nasty little bugs with things like JS that crop up on certain minor versions of browsers or unusual browsers. Using window.onerror and XMLHttpRequest we can log anything that's not syntax related into a database and keep on top if these "niggles".
I started writing something called phpMyAjax that I actually put on SF but haven't really continued far with it. It was the equivalent of the command line MySQL client but with ANSI-appearance colors and written in JavaScript

Maybe I'll have another play with it again - it needs some major refactoring before I can feel happy with it.