Midori is an ultra-lightweight JavaScript framework that gets the job done without getting in your way.
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.
qooxdoo is a comprehensive and innovative framework for creating rich internet applications (RIAs). Leveraging object-oriented JavaScript allows developers to build impressive cross-browser applications. No HTML, CSS nor DOM knowledge is needed
The Spry framework for Ajax is a JavaScript library that provides easy-to-use yet powerful Ajax functionality that allows designers to build pages that provide a richer experience for their users. It is designed to take the complexity out of Ajax and allow designers to easily create Web 2.0 pages.
Dojo is an Open Source DHTML toolkit written in JavaScript. Dojo aims to solve some long-standing historical problems with DHTML which prevented mass adoption of dynamic web application development
MochiKit is a highly documented and well tested, suite of JavaScript libraries that will help you get shit done, fast.You re unlikely to find any JavaScript code with better documentation than MochiKit. 
jQuery is a fast and concise JavaScript Library that simplifies HTML document traversing, event handling, animating, and Ajax interactions for rapid web development. jQuery is designed to change the way that you write JavaScript.
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.
script.aculo.us provides you with easy-to-use, cross-browser user interface JavaScript libraries to make your web sites and web applications fly.
It s an add-on to the fantastic Prototype framework. 