There are some popular frameworks, which do you prefer?
Adobe Spry-Ajax Framework
documentation is good
Easy to use
good community both in terms of conversation and plugin development
easy-to-use Ajax (I love the $.ajaxSetup() function)
Nice event handlers
filtering your selection
did I mention chaining?
Small (only 30 KB)
Nice little built-in effects.
excellent widget system
Modules done right with all necessary goodies:
Lazy loading of modules dynamically.
Possibility to extract only necessary modules and build a custom one-file profile.
Asynchronous loading of modules if desired.
Respond to an event
Request Data / Manipulate Services (Ajax)
Add domain specific information to the ajax response.
Update the DOM
Integrated Browser, Selenium, and Rhino Testing
YUI for a complete, professional looking, enterprise oriented widget toolkit.
You can download each of these scripts individually from the developer.yahoo.com site.
ExtJs: ExtJs offers its library under LGPL. you can use it in a commercial web site, without having to open up your source code as well. BUT if you make changes to ExtJs, you have to provide the possibility to download the source code to your changed ExtJs.