Ajax Patterns and Frameworks

Javascript
Popular:
Javascript Multipurpose Frameworks Broader-scope frameworks (e.g. Dojo, BackBase).
Javascript Remoting Frameworks Browser-Server Web_Remoting, i.e. XMLHttpRequest wrappers and IFrame wrappers.

Specialised:
Javascript Effects Frameworks Visual Effects.
Javascript Flash Frameworks Javascript-Flash Integration.
Javascript XML Frameworks Dealing with XML, XSLT, Xpath, and possibly Web Remoting. (e.g. GoogleXSLT).
Javascript Specialised Frameworks Frameworks that don't fit any catgory above, e.g. drag-and-drop or widget libraries.

Server-Side and Hybrid Frameworks
Multi-Language Ajax Frameworks
Coldfusion Ajax Frameworks
DotNet Ajax Frameworks
Java Ajax Frameworks
Lotus Notes Ajax Frameworks
Lisp Ajax Frameworks
Perl Ajax Frameworks
PHP Ajax Frameworks
Python Ajax Frameworks
Ruby Ajax Frameworks
XUL Ajax Frameworks

Go to the AjaxPatterns.org website for more details