Various JavaScript Libraries and Frameworks

*jQuery - 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. jQuery is supported in Visual Studio 2010 with intellisense.
jquery.com/

*jQueryUI - provides abstractions for low-level interaction and animation, advanced effects and high-level, tameable widgets, built on top of the jQuery JavaScript Library, that you can use to build highly interactive web applications.
jqueryui.com/

*Modernizr - an open-source JavaScript library that helps you build the next generation of HTML5 and CSS3-powered websites.
modernizr.com/

*PhoneGap -
HTML5 app platform that allows you to author native applications with web technologies and get access to APIs and app stores. PhoneGap leverages web technologies developers already know best... HTML and JavaScript
phonegap.com/

*KnockoutJS - Simplify dynamic Javascript UIs by applying the MVVM (Model - View - View Model) pattern.
knockoutjs.com/

BackboneJS - supplies structure to JavaScript-heavy applications by providing models with key-value binding and custom events, collections with a rich API of enumerable functions, views with declarative event handling, and connects it all to your existing application over a RESTful JSON interface.
documentcloud.github.com/backbone/

*CoffeeScript


*Cassette

*NodeJS - a platform built on Chrome's JavaScript runtime for easily building fast, scalable network applications. Node.js uses an event-driven, non-blocking I/O model that makes it lightweight and efficient, perfect for data-intensive real-time applications that run across distributed devices.
nodejs.org/

*Sencha ExtJS - Featuring expanded functionality, plugin-free charting, and a new MVC architecture it's the best Ext JS yet. Create incredible web apps for every browser.
sencha.com/products/extjs/

*Sencha Touch - Sencha Touch allows you to develop mobile web apps that look and feel native on iPhone, Android, and BlackBerry touch devices.
sencha.com/products/touch/

!Appcelerator -

appcelerator.com/

!MooTools - 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.
mootools.net/

Prototype - JavaScript Framework that aims to ease development of dynamic web applications. Featuring a unique, easy-to-use toolkit for class-driven development.
prototypejs.org/

YUI - 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.
developer.yahoo.com/yui/

Dojo - Dojo saves you time, delivers powerful performance, and scales with your development process. It's the toolkit experienced developers turn to for building superior desktop and mobile web experiences.
dojotoolkit.org/

Processing.js - Processing.js is the sister project of the popular Processing visual programming language, designed for the web. Processing.js makes your data visualizations, digital art, interactive animations, educational graphs, video games, etc. work using web standards and without any plug-ins. You write code using the Processing language, include it in your web page, and Processing.js does the rest. It's not magic, but almost.
processingjs.org/

Right.js- a modular JavaScript framework. It has a very skiny (15k gzipped) core that has all the standard features, like dom-manipulation, animation, forms, cookies, events handling and so on. But the core in RightJS is not just a closed monolith, on the contrary, it is an open structure, much like Ruby or Python. It provides you with an environment and basic building blocks, which you can reuse, patch, bend and hack, making the core itself fit your application.
rightjs.org/