A serious contender. Event processing. The biggest, oldest and one with most support. That is there's more cool widgets, gizmos and programs written out with this stuff than anyhthing else. If you're looking to write something, first thing, check to see if somebody else has already written it. Or something close to it. It's surprising how much stuff there is already for jquery.

Extremely comprehensive.

ExtJs is quite well done, but there are some license issues for some people. There are versions that have an LGPL license and one that's proprietry, you can pick which version to download and then you're bound by that particular license.

Yahoo's entry into the JS framework arena. Yahoo?!? Yeah, I know I know, but, have a good look at it, they have some clever people and it's very well done and quite well thought out. Note also that it's a Yahoo language that runs in some of the smart TV' (like the Samsung for example). As dorky as the yahoo home page is, their developers have an understanding of programming every bit as Google's. Thats the good news, the bad news is, there's YUI2 and a later, greater, rewritten, faster YUI3. Saldly I can't get it to work properly.

Another JavaScript framework. script.aculo.us is a widget library built on prototype.