prototype.js is a free toolkit for writing ajax applications. Works great on IE/Firefox. Also claims to support Safari.
Lastly, I’ll mention Zimbra’s Ajax Library, which is probably worth a look if you are just getting started simply because their demos are so impressive. Because Zimbra is an applications company, the library is buried within their source code, and they don’t spend a ton of time making it easy for developers. So it will a take a little more time to get started with this one, which is the reason I have yet to try it myself.
If you are searching for ajax info, you might want to check out the Ajax Frameworks page at ajaxpatterns.org.