I did try DOJO (which I think is backed by IBM), but found it too hard to understand. MooTools is very popular, and has a small footprint but I find their documentation lacks any real examples, or code that you can copy-paste or hack apart. MochiKit has a lot of buzz, but I find it does a very similar job to jQuery.
I find jQuery has a lot of examples, and there are already 2 books out there on this framework.
Although I’ve only been able to do small-scale examples of jQuery, I’m hoping to learn how to integrate jQuery with PHP/MySQL and deliver some of those really nice effects that you’ve seen everywhere else.