dojoThis one is really extensive and tries to achieve anything and everything. It seems easy to grasp and I was able to get going in less than a few minutes. But given the fact that it is really extensive it also adds to the weight. I don't think I would be using the complete library in any of my projects but if used as a learning resource it can be really great.
ExtJSThis is one library I have seen from the very beginning I have always liked it. The toolkit is really professional looking and seems to fit the bill but the only hitch is the license, its under GPL3. If you don't mind paying then you can get it with a commercial license. This is one of the best library you could use.
YUIYUI is another library I've liked but again this is one of the libraries that seems bloated. Its not really bloated but I've never seemed to like it. It does get the work done and is also easy to learn. But given the size it always seems complex even though it is not. I will have to give it another good look and maybe I might end up liking it.
JQueryI have tried it earlier but could never seem to like it. But when I tried it this time around I fell in love with it. All I can say is that its awesome to say the least. The UI part of JQuery is still work in progress but it seems to fit the bill for me.
prototypeThis library also seems to have grown a lot both in terms of size and features since the last time I checked it. Not really tried it enough to have a viewpoint about it.
NOTE: This post is still a work in progress. It might change.