Linb - Provides an Object Oriented framework supporting AJAX and multilingual interface. Discussion group, download and documentation. - http://code.google.com/p/linb/
Ext - Provides an AJAX library and UI components. - http://extjs.com/
Mootools - Offers a lightweight web2.0 JavaScript framework. - http://mootools.net/
Behaviour - Offers a script allowing the use of css selectors applying the language behaviours. - http://bennolan.com/behaviour/
MochiKit - Provides a suite of libraries taken from Python. Documentation and download. - http://www.mochikit.com/
Open Rico - Offers visual effects, styling, drag and drop and ajax functions. Requires Prototype. - http://www.openrico.org/
jQuery - A fast, concise, library that simplifies how to traverse HTML documents, handle events, perform animations, and add AJAX. - http://jquery.com/
Prototype - Provides class-style Object Oriented and AJAX, freely distributable under the terms of an MIT-style license. - http://www.prototypejs.org/
Script.aculo.us - A collection of Web 2.0 style JavaScript libraries that help web developers to easily add visual and ajax effects to projects. Requires Prototype. - http://script.aculo.us/