General Computer Science
These books are mostly focused on computer science, but many of them also have excellent sections on Artificial Intelligence. The information on computer science is also quite crucial to understanding Artificial Intelligence.

Introduction to Data Structures and Algorithms Analysis with C++

This is an excellent textbook for learning many concepts of computer science. It covers many interesting topics that relate to Chess and Go programming such as linked lists, hashing, stacks, queues, networks, and trees. It has many pictures and diagrams to help explain everything clearly, and it gives code frameworks for programming the algorithms. It is quite a good reference as well.
 

The New Turing Omnibus

This book is almost completely theory and math, but it is very thorough and explanatory. Many interesting topics show up including minimax tree searches, encryption, error correcting, and artificial life. It has a large amount of material on Turing machines, finite-state machines, and NP-Complete problems. It's a great book for an overview on many aspects of theoretical computer science, and it also makes a handy reference.
 

Selected Papers on Computer Science

Written by the famous Donald Knuth, this book is a sampling of Knuth's less technical works, ranging from the relationship between Computer Science and Math to the early history of Computer Science, from Babylonia to John Von Neumann. His conversational tone makes this an enjoyable, easy read.
 

Cognitive Science
In order to build an intelligent system that can emulate or even exceed human intelligence, it is very important to first understand human intelligence itself. In recent years, great strides have been made in the field of Cognitive Science -- the study of human thought. In particular, the areas of Linguistics and Vision have made stunning progress, resulting in such programs as Dragon NaturallySpeaking.

G�del, Escher, Bach: An Eternal Golden Braid

Although it is categorized in this site under Cognitive Science, this Pulitzer Prize-winning book touches on everything from music to chemistry to mathematcs and philosophy. It isn't a systematic study of the human mind, but it is a book of musings and profound ideas about human thought that have their applications in many different fields even today, more than 20 years after it was published. Entertaining, thought-provoking, and easy-to-read, this book has introduced many to the wonders and joys of the human mind. It is very much recommended.
 

How the Mind Works

This best-selling book tries to summarize the current situation of Cognitive Science. The author avoids technical jargon, but still manages to present some astounding examples and explanations of a variety of mental phenomenon, from visual illusions to the reason memory fades. All throughout the book, the author tries to defend the Computational Theory of the Mind; he is only moderately successful at this, sometimes dancing around the point, but that shouldn't stop you from enjoying the plethora of content this book can offer.
 

The Language Instinct

This is a very easy-to-read book that's full of information on the progress of linguistics after Noam Chomsky's brilliant work. It dispels common myths and illuminates all kinds of new hypotheses to the public. The reading is not very technical, so the book is a great introduction to linguistics for anyone.

Game programming
These books cover how to program Go, Chess, and other games. Some of these books are analyses of board games from a mathematical or computer science oriented point of view, while others are concerned with the AI of games.

AI Game Programming Wisdom

This book is a great addition to the game programming community. It deals with AI concepts that can be implemented in games, such as pathfinding algorithms, finite state machines, decision-making algorithms, and even the genetic algorithm.
 

Mathematical Go

This book covers the endgame of Go using combinatorial game theory. If you haven't already learned combinatorial game theory, it tries to introduce the topic gently, but it can get confusing sometimes. There are a few misprints scattered throughout, but this book, I think, is still worth the money. It has an excellent coverage of the mathematical rules of Go, and it is quite good at defining sente and gote in mathematical terms.
 

The Turk: The Life and Times of the Famous Eighteenth-Century Chess-Playing Machine

This engrossing history examines the craze and philosophy surrounding the Mechanical Chess-Playing Turk of Wolfgang von Kempelen, and correlates it to the modern movement with Artificial Intelligence and Chess computers. In the process, the book examines both machine intelligence and human relationships to seemingly intelligent automata.

AI and Artificial Life
These books cover general topics in Artificial Intelligence as well as topics in Artificial Life and cellular automata (such as Conway's Game of Life).

A New Kind of Science

Stephen Wolfram's controversial new book claims that cellular automata will completely change the face of all of the sciences, and that for the past 300 years, science has been doing things wrong. Some claim that this book is astoundingly refreshing, others dismiss it as inconsequential and overhyped. The book is written in fairly non-technical language, although if you want to delve into the details, appendixes and notes are filled with extra information.
 

The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics

The controversial book by Roger Penrose, a leading mathematician and physicist. The book tries to refute once and for all the theory of "Strong AI", which believes that AI can, eventually, create a computer with a mind of its own on the par of a human mind. As can be seen from the title, the book delves into a wide range of topics including AI, philosophy, mathematics, and physics.