Introduction to Ajax Frameworks
Healthy Warning: Its an introduction note to the Ajax beginners and late adopters to choose from the top frameworks. If you are an experienced d00d , don’t waste your time reading this 
Prototype for downloads and more info
First of all, Prototype can not be called as an exclusive Ajax framework. It should be called as a Utility framework powered with Ajax.
Sam Stephenson created this amazing library of functions to ease our JavaScript development practices for the web developers. Best part of protoype are the shortcuts to handle the DOM elements, form elements, array and many more.
Prototype is backed with rich Ajax support. Periodical executor and ability to execute a js function on ajax returned html makes your life easier.Another great utility comes with the prototype is Try.these functions. This function will attempt to execute one path of code until it encounters an error, and then switch to the next path, way better than writing a browser detection code every time. Other than that this framework is powered with features like, key press event handler, mouse handler,class creator and even comes with ability to attach an event to the DOM using observe.
Scriptaculous downloads & more info
It is a collection of Web 2.0 style JavaScript libraries that help web developers add AJAX functionally to projects.The power of AJAX allows for rich user interaction without the trouble that has bugged traditional web applications. Building upon the wonderful Prototype JavaScript library, script.aculo.us provides you with some great additional value like adding some cinematic effects into your RIA efforts.
Google Web Toolkit downloads & more info
Google Web Toolkit (GWT) is a Java software development framework that makes writing AJAX applications like Google Maps and Gmail easy for developers who don’t speak browser quirks as a second language. It comes with browser history management features that will compliment the back button issues in normal ajax application and it also have the ability to integrate with your JUNIT test cases. This is more recommended to developers who are more familiar with Java or C++.
YUI Library downloads & more info
The Yahoo! User Interface Library is a set of utilities and controls, 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. It even have some of the coolest colorpicker and some other cool ajax ready to use features. Y! comes with features like darg and drop, tooltip, containers, widgets and many many more goodies. Y! is very serious about this community and its backed up with very good documentation and tutorials. I liked this one after prototype (thats just personal opinion 
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Dojo is the Open Source JavaScript toolkit that helps you build serious applications in less time. It fills in the gaps where JavaScript and browsers don’t go quite far enough, and gives you powerful, portable, lightweight, and tested tools for constructing dynamic interfaces.
Dojo powered with widgets like SortableTable, TitlePane, Form validation,Menus and menu bars and Google & Yahoo maps . If your a mashup developer, you may like Dojo over other frameworks.
Rico Downloads & More info
Rico provides a very simple interface for registering Ajax request handlers as well as HTML elements or JavaScript objects as Ajax response objects. Multiple elements and/or objects may be updated as the result of one Ajax request. Rico also powered with features like cinematic effects and drag & drop.
Atlas downloads & more info
I never used this. But my Brother did in his application.This new Web development technology from Microsoft integrates client script libraries with the ASP.NET 2.0 server-based development framework. In addition, “Atlas” offers you the same type of development platform for client-based Web pages that ASP.NET offers for server-based pages. And because “Atlas” is an extension of ASP.NET, it is fully integrated with server-based services. “Atlas” makes it possible to easily take advantage of AJAX techniques on the Web and enables you to create ASP.NET pages with a rich, responsive UI and server communication. However, “Atlas” isn’t just for ASP.NET. You can take advantage of the rich client framework to easily build client-centric Web applications that integrate with any backend data provider. It required Microsoft .NET Framework Version 2.0 .
I shall try Atlas on my Home PC one of these days
There are more tools like xajax, sajax, tiny ajax, MochiKit, xoad, haxe etc.
Personally if you ask my favorite, I go with the prototype for its amazing set of utility functions and the powerful ajax features. Plus a large community is using ruby on rails which integrated prototype. Opensource community already demanded adding prototype to core js libraries. So someday you should not be surprising to see prototype features on js core. If you are a .net guy, I badly want you to try atlas. It seems like very promising and cool. My second option will be YUI for its simplicity and power packed features and widgets.
