The following are books that I have read and found useful.

The Art of Game Design : A Book of Lenses
by Jesse Schell

If you are serious about designing great games you need to read this book.  It is the best one I have read with respect to designing a game.  It covers a wide range of topics including understanding the player, game mechanics, theme, balancing, and so much more.  It also contains a series of “lenses” which are questions you can ask yourself about your game in order to better understand it and to improve it. 

The Game Inventor’s Guidebook
by Keith Meyers

If you are new to game design and to the game industry this is a great book to help further your education and to inspire you to keep going. It has the background story of several successful games as well as interviews with well known people within the industry. It gives inside information on how the industry works and on the steps you need to take to be successful.

Paid to Play: The Business of Game Design
by Brian Tinsman

A good book about designing games. This book by the inventor of the extremely popular “Apples to Apples” game gives an overview of the industry and some specifics on designing great games.

About Jenga
by Leslie Scott

This is an interesting book by the inventor of the extremely popular game “Jenga”. It describes in detail the journey she took when bringing her game to market. It may not help you design a great game, but it will give you the inspiration to keep on trying and to never give up.

Probability for Dummies
by Deborah Rumsey-Johnson

Like it or not, math is an important tool for game developers (I happen to like it). When trying to balance your game a good understanding of probability can be very helpful. I had attempted to read several math text books on probabilities so that I could better understand and use them. Unfortunately I would never seem to make it past the first chapter before the book became way to “mathy” (I know it is not a real word, but it sounded good). This is the first probability book I made it through and was able to honestly say “I get it now”. If you are interested in learning probabilities this is a great place to start.