This is the complete reference for MooTools with in-depth details and examples on every method and class in the library.
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The online MooTorial gives a brief overview of every class and method in MooTools with examples you can run in your browser. While not nearly as complete as the book, the online tutorial is a great place to start.

Clientcide is the companion to the MooTorial, offering the largest single collection of MooTools plugins on the net and a blog covering client-side technology in general.

Other Tutorials and Resources

MooTools 1.2 Beginner's Guide (a book)
A beginner's guide to MooTools, this book authored by Garrick Cheung and Jacob Gube is a nice place to start.
Ryan Florence's Blog
Ryan's Blog is dedicated entirely to MooTools oriented tutorials and is a great place to get started learning new techniques.
Up the Moo Herd

This series of tutorials is excellent, in some ways better than the mootorial especially for people who are moderate JavaScript users - not beginners but not experts. A must read.

A complete walk through of MooTools 1.2 (that you can download if you like). This walkthrough is a little more clearly aimed at teaching new-comers how to use the framework in a step-by-step introduction than the Mootorial is. A good companion if you're new to frameworks or MooTools.
Using Custom Events in Mootools
A nice overview of using Events in classes.
JavaScript Mouse Movement Recording Tutorial
A short example of how to write a MooTools class to capture mouse movements.
Chaining with MooTools 1.2
An in-depth tutorial of how to use the Chain class.
MooTools 1.2: Swiff (MooTools Blog)
An overview of the Swiff functionality in MooTools 1.2.
MooTools Classes: How to use them (MooTools Blog)
An entry-level introduction to using classes.
Element Storage (MooTools Blog)
This article describes the usage of this great new feature, as well as why it was developed, and how it can be used to keep your applications organized and efficient.

MooTools 1.11 Tutorials

These are still useful, though be aware that they include examples that are outdated.

How Well Do You Know MooTools?
This is a nice collection of "right way" / "wrong way" comparisons. Unfortunately it hasn't been updated for MooTools 1.2 (Element.setProperty is now just Element.set, for example), but it's still informative. See also the second part.(MooTools 1.11)
MooTools: JSON explained
Bas Wenneker gives an overview of how to used JSON and Ajax (aka Request) to make your content more dynamic. (MooTools 1.11)
Beauty in Design - Increasing User Experience With JavaScript
A nine part series covering animation, ajax, classes, and more. This is a little old now and was created for MooTools 1.11 so some of it is no longer applicable.