It really depends what you are after. If you want to add a couple of small tweaks nothing that big. Then I agree with MarkR, most libraries are too heavy going.
However, if you are implementing something bigger (like i am here) then not using a library would require so much extra developing.
I would not recommended the libraries that I used in the end in that project.
From what I've used/seen;
Prototype - very useful
script.aculo.us - bloated and a bit bugggy at times
Yahoo! UI - Looks good but I've not used it much
ExtJS - VERY powerful but very big and only free for non-profit.
I've heard good things about JQuery and dojo too but not tried them yet. Also mooFX is a powerful small JavaScript effects library.
If you want something to help you with the actual PHP and handling requests, this is usful xajax
So i guess, if I was starting a project now I'd try with Yahoo! UI - unless it was just something small then I'd do it myself.
... i'm sure there are more I've forgotten to mention.