jQuery

jQuery is a compact but powerful framework that substantially reduces the amount of code you have to write for DOM manipulation and Ajax requests. It was originally written by John Resig, who is a JavaScript evangelist for the Mozillla Corporation, and now developers all over the world help maintain, extend and write plug-ins for this widely-adopted framework.

YUI

The YUI is an extensive library of code that provides the foundation for large-scale, cross-browser compatible and accessible Web sites and online applications. It was originally developed for the Yahoo! portal, arguably the world’s largest Web site.

Spry

Adobe's Spry framework provides a large library for data management, interface components, Ajax and validation. Like YUI, the Spry framework has been developed for accessibility and cross-platform robustness. It can also be accessed as a Dreamweaver extension, so that Spry functionality can be implemented by non-programmers through Dreamwever's Design View.

Prototype

Prototype and jQuery are similar in that they both provide a shorthand syntax for key JavaScript accessing the DOM and interating over data sets. Prototype tends to be favored over jQuery by some programmers (especially Rails programmers) who prefer its more elegant interpretation of JavaScript and the clean implementation of its API.