The essential books for animators and character designers...

Or... how I spent a lot of money in order to be better educated.

Here are the first 3 books I think animators especially should get.

Force: Dynamic Life Drawing for Animators
Draw the Looney Tunes

Animator's Survival Kit

Force: Dynamic Life Drawing should be studied first, along with Draw the Looney Tunes (provided that you have been studying drawing already, beyond the basics). Both books combined form what I like to call "The Art and Zen of Stylized Drawing", because they are not the standard drawing manuals that describe how to perfectly make a complex character from a sphere: rather, these teach you about the head game.

Draw the looney tunes looks like a simple book, but actually it is essentially the cartoon manual granted to new Warner Bros. animators, who are just starting to learn. It is all about the proper psychology to drawing, starting with the line of action, followed by advanced concepts like rhythm. It is definitely a text that requires you take each page slowly, drinking in all of the info it is giving you.

Mattesi's book, Force: Dynamic Life Drawing essentially teaches you a specific process and thinking behind life drawing. It teaches you how to create some very pushed and exagerrated drawings, more to find the active forces in the image rather than the realistic edges.

I'd suggest supplementing either of these with something that keeps you grounded in realistic life drawing as well... It could be dangerous to make yourself a one-trick-pony early on, and it is good to have as varied a level of expertise as possible.

Last, but without a doubt not least, Richard William's Animator's Survival Kit is now your Bible as an animator. It is the holy writ in regards to motion and timing, and is indispensable as a resource and guide. No animator should be without their own copy of this book.