Prototype
Prototype is a JavaScript framework that aims to ease development of dynamic web applications.

Homepage: http://prototype.conio.net

Documentation:
http://blogs.ebusiness-apps.com/jordan/pages/Prototype%20Library%20Info.htm
http://www.sergiopereira.com/articles/prototype.js.html
http://wiki.script.aculo.us/scriptaculous/show/Prototype

Rico
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.

Homepage: http://openrico.org/rico/home.page
Documentation: http://openrico.org/rico/docs.page
Demos: http://openrico.org/rico/demos.page

MochiKit
MochiKit is a highly documented and well tested, suite of JavaScript libraries that will help you get things done, fast.

Homepage: http://www.mochikit.com/
Documentation: http://www.mochikit.com/doc/html/MochiKit/index.html
Demos: http://www.mochikit.com/demos.html

Dojo Toolkit
Dojo is an Open Source toolkit that allows you to easily build dynamic capabilities into web pages and any other environment that supports JavaScript. Dojo provides components that let you make your sites more useable, responsive, and functional.

Homepage: http://www.dojotoolkit.org/
Documentation: http://dojotoolkit.org/docs/
Demos: http://dojotoolkit.org/examples/

Behaviour
Separate Structure (xhtml) from Behavior (javascript)

Homepage: http://bennolan.com/behaviour/

Solvent
The Solvent is a cross-browser AJAX application toolkit written in JavaScript. The Solvent is provided as modules or as an entire toolkit. The projects focus is to promote robust web applications and enable rapid web development.

Homepage: http://sourceforge.net/projects/solvent/
Documentation: http://sourceforge.net/docman/?group_id=144164

Moo.FX
moo.fx is a superlightweight, ultratiny, megasmall javascript effects library, written with prototype.js.

Homepage: http://moofx.mad4milk.net/
Demo: http://moofx.mad4milk.net/tests.html

WZ_DradDrop
A Cross-browser JavaScript DHTML Library which adds Drag Drop functionality to layers and to any desired image

Homepage: http://www.walterzorn.com/dragdrop/dragdrop_e.htm

WZ_jsGraphics
High Performance JavaScript Vector Graphics Library.

Homepage: http://www.walterzorn.com/jsgraphics/jsgraphics_e.htm

overLIB
overLIB is a JavaScript library created to enhance websites with small popup information boxes (like tooltips) to help visitors around your website.

Homepage: http://www.bosrup.com/web/overlib/
Documentation: http://www.bosrup.com/web/overlib/?Documentation
Command reference: http://www.bosrup.com/web/overlib/?Command_Reference

Scriptaculous
Javascript visual effects, togather with prototype.js

Homepage: http://script.aculo.us/

SACK
Simple AJAX Code-Kit

Homepage: http://twilightuniverse.com/projects/sack/