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There's no doubt in my mind, the YUI library is the one to use. It seems to provide the cleanest and most complete approach to "low-level" browser needs without cluttering up the language with it's particular approach to JS. It also has done an incredible effort in categorizing browser compatibility and making that known to the dev and end user. As if that wasn't enough, there is also the amazing comfort knowing that this was born out of need, and is deployed at visible Yahoo properties where they will be dealing with any sort of browser configuration and issue...

After that, I think Dojo also worth looking at, as it has a very similar high-level approach to their api design. Brendan Eich and IBM also seem to favor them which is noteworthy.

We've used DOJO in a few places internally, but I've also been hesitant about all the stuff you have to include (a lot of files). We use scriptaculous here, but I will definitely check out YUI.