1. jQuery and jQuery UI
2. Prototype and Script.aculo.us
4. Moo Tools
Personally I like both Prototype and jQuery, but jQuery has a lot more useful plugins to offer. jQuery is perhaps the most popular one currently, check out the slides from Yehuda Katz from the Rails Conference here
I haven’t checked out any JS frameworks yet but I’m considering checking out jQuery as I’m starting to do more complex JS animations and I think it would seriously cut down dev time for such tasks.
The overhead of the framework files is always something that kind of deters me, but since Google is hosting jQuery now I may look at it more seriously because that’s a copy that could be cached on quite a number of machines.