Here is the roundup of popular javascript libraries and frameworks. Feel free to comment, suggest and share your thoughts.

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. Get it Here.
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The driving force behind Ext JS is Jack Slocum, who is a respected JavaScript developer. The Ext JS project sprouted from a desire to extend functionality offered by the Yahoo! User Interface (YUI) Library.
A key aspect of the YUI Library is the cross-browser support, which you’ll also find in Ext JS. This allows you to build Web applications without worrying about the target browser.
Ext JS boasts excellent performance. The framework is fully object-oriented and extensible. Along with its excellent presentation, Ext JS’ features are ready to use once you download and install it.
Features
Ext JS includes various controls such as a message box, combo box, data grid and toolbars. In addition, layout managers allow you to specify how elements are presented on a page. More features are available for working with forms and windows. Adobe has introduced a new platform, AIR, for deploying HTML/JavaScript applications to the desktop. One of their feature applications is Fresh, an RSS feed reader built with Ext.
Mike Chambers, Senior Product Manager at Adobe says: “Basically, if you want to build Apollo applications using HTML / JavaScript, then this is the library you should start with. Not only does it provide lower level JavaScript functionality, it also provides a complete UI component toolkit, and effect library.”.

Downloads and Samples
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jQuery is a fast, concise, JavaScript Library that simplifies how you traverse HTML documents, handle events, perform animations, and add Ajax interactions to your web pages. jQuery is designed to change the way that you write JavaScript.
“You start with 10 lines of jQuery that would have been 20 lines of tedious DOM JavaScript. By the time you are done it’s down to two or three lines and it couldn’t get any shorter unless it read your mind.” – Dave Methvin

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.
MooTools code respects strict standards and doesn’t throw any warnings. It’s well commented and has meaningful variable names: a joy to browse and a snap to understand.
moo.fx is a superlightweight, ultratiny, megasmall javascript effects library, to be used with prototype.js or the mootools framework.
It’s very easy to use, blazing fast, cross-browser, standards compliant, provides controls to modify any CSS property of any HTML element, including colors, with builtin checks that won’t let a user break the effect with multiple, crazy clicks. Optimized to make you write the lesser code possible, the new moo.fx is so modular you can create any kind of effect with it.
Download MooTools Framework, See the Demos. Get Moo.FX
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The Yahoo! User Interface (YUI) Library is a set of utilities and controls, written in JavaScript, for building richly interactive web applications using techniques such as DOM scripting, DHTML and AJAX. The YUI Library also includes several core CSS resources. All components in the YUI Library have been released as open source under a BSD license and are free for all uses.
Features
Two different types of components are available: Utilities and controls. The YUI utilities simplify in-browser devolvement that relies on cross-browser DOM scripting, as do all web applications with DHTML and AJAX characteristics. The YUI Library Controls provide highly interactive visual design elements for your web pages. These elements are created and managed entirely on the client side and never require a page refresh.
utilities available:
Controls available:
Download and more information: here

MochiKit is a highly documented and well tested, suite of JavaScript libraries that will help you get shit done, fast. We took all the good ideas we could find from our Python, Objective-C, etc. experience and adapted it to the crazy world of JavaScript.
Reliable
MochiKit has HUNDREDS of tests. We build real applications with this thing. So even though development can move fast, we make sure to get tests written. This also makes platform compatibility issues much easier to detect and resolve than the “guess and check” style of quality assurance seen in some of the other libraries out there. It’s not broken.
Documented
You’re unlikely to find any JavaScript code with better documentation than MochiKit. We make a point to maintain 100% documentation coverage for all of MochiKit at all times. You don’t have to fumble around reading our source code or leafing through examples to find out how something works.
Evolutionary
MochiKit can adapt to anything you throw at it. It makes no assumptions about how your code needs to act, and it has hooks (by way of the the adapter registries) that makes sure that you can define your own comparisons, programmer representations, iterators, or DOM node coercion for any object in any way you wish. We’ll gladly serve you all the Kool-Aid you want, but we’re not going to make you drink any.
Download and here are the Demos.

qooxdoo is a comprehensive and innovative Ajax application framework. Leveraging object-oriented JavaScript allows developers to build impressive cross-browser applications. No HTML, CSS nor DOM knowledge is needed.
It includes a platform-independent development tool chain, a state-of-the-art GUI toolkit and an advanced client-server communication layer.
Features
Furthermore there is the possibility to call the target function in any object context. (The default is the object which defines the event listener.) The event system normalizes differences between the browsers, includes support for mousewheel, doubleclick and other fancy stuff. qooxdoo also comes with an advanced capture feature which allows you to capture all events when a user drags something around for example.
Downloads and more information here. Have a look at the Demos too.
Dojo allows you to easily build dynamic capabilities into web pages and any other environment that supports JavaScript sanely. You can use the components that Dojo provides to make your web sites more usable, responsive, and functional. With Dojo you can build degradable user interfaces more easily, prototype interactive widgets quickly, and animate transitions. You can use the lower-level APIs and compatibility layers from Dojo to write portable JavaScript and simplify complex scripts. Dojo’s event system, I/O APIs, and generic language enhancement form the basis of a powerful programming environment. You can use the Dojo build tools to write command-line unit-tests for your JavaScript code. The Dojo build process helps you optimize your JavaScript for deployment by grouping sets of files together and reuse those groups through “profilesâ€.
Features
Download and more information here. See it in Action.
