Personally I would rather not use JavaScript libraries however there is a whole lesson designated to this subject in the CIW: JavaScript Specialist course material.
Here's what I've browsed over from Wikipedia:
jQuery is a cross-browser JavaScript library designed to simplify the client-side scripting of HTML. It was released in January 2006 at BarCamp NYC by John Resig. Used by over 52% of the 10,000 most visited websites, jQuery is the most popular JavaScript library in use today. jQuery is free, open source software, dual-licensed under the MIT License or the GNU General Public License, Version 2. jQuery's syntax is designed to make it easier to navigate a document, select DOM elements, create animations, handle events, and develop Ajax applications. jQuery also provides capabilities for developers to create plug-ins on top of the JavaScript library. This enables developers to create abstractions for low-level interaction and animation, advanced effects and high-level, theme-able widgets. The modular approach to the jQuery library allows the creation of powerful dynamic web pages and web applications. Microsoft and Nokia have announced plans to bundle jQuery on their platforms, Microsoft is adopting it initially within Visual Studio for use within Microsoft's ASP.NET AJAX framework and ASP.NET MVC Framework while Nokia has integrated it into their Web Run-Time widget development platform. jQuery has also been used in MediaWiki since version 1.16.
I've already found the animation example, and the validate plugin to be of help.
MooTools (My Object-Oriented Tools)[1] is a lightweight, object-oriented, JavaScript framework. It is released under the free, open-source MIT License.[2] It is used on more than 5% of all websites, and is one of the most popular JavaScript libraries.
It uses components, and has an object oriented syntax for designing class objects.
e.g.
var Animal = new Class({
initialize: function(name) {
this.name = name;
}
});
var Cat = new Class({
Extends: Animal,
talk: function() {
return 'Meow!';
}
});
var Dog = new Class({
Extends: Animal,
talk: function() {
return 'Arf! Arf';
}
});
var animals = {
a: new Cat('Missy'),
b: new Cat('Mr. Bojangles'),
c: new Dog('Lassie')
};
Object.each(animals, function(animal) {
alert(animal.name + ': ' + animal.talk());
});
Dojo Toolkit is an open source modular JavaScript library (or more specifically JavaScript toolkit) designed to ease the rapid development of cross-platform, JavaScript/Ajax-based applications and web sites. It was started by Alex Russell, Dylan Schiemann, David Schontzler, and others in 2004 and is dual-licensed under the modified BSD license or the Academic Free License (≥ 2.1). The Dojo Foundation is a non-profit organization created with the goal to promote the adoption of the toolkit.
It mostly uses widgets e.g. gauges, graphs, charts, menus, tables etc.