Prototype

Prototype is a JavaScript Framework that aims to ease development of dynamic web applications.

Featuring a unique, easy-to-use toolkit for class-driven development and the nicest Ajax library around, Prototype is quickly becoming the codebase of choice for web application developers everywhere.

MooTools

MooTools is a compact, modular, Object-Oriented JavaScript framework designed for the intermediate to advanced JavaScript developer. It allows you to write powerful, flexible, and cross-browser code with its elegant, well documented, and coherent API

EXTJS

Ext JS is a cross-browser JavaScript library for building rich internet applications.

• High performance, customizable UI widgets
• Well designed, documented and extensible Component model
• Commercial and Open Source licenses available

dojotoolkit

Like every Ajax toolkit, Dojo gives you a rich set of utilities for building responsive applications.

scriptaculous

script.aculo.us provides you with easy-to-use, cross-browser user  interface JavaScript libraries to make
your web sites and web applications fly.

YUI Library

The YUI Library is a set of utilities and controls, written with JavaScript and CSS, for building richly interactive web applications using techniques such as DOM scripting, DHTML and AJAX. YUI is available under a BSD license and is free for all uses.

YUI is proven, scalable, fast, and robust. Built by frontend engineers at Yahoo! and contributors from around the world, it’s an industrial-strength JavaScript library for professionals who love JavaScript.