There are thousands of books written about chess, more than for any other game. There is simply no way to read them all, as more are published every year. Here is a list of the ten books universally regarded as absolutely essential to any chess player. You will not find any opening "repertoire" books or "Easy guide to..." books or anything like that. These are not shortcut books, they are serious works by serious authors for serious students. Most advanced players will own 9 out of the 10 at least. They have not been numbered because that would imply that one book is more important than another. So here you have them:
Title: My System
Author: Aaron Nimzovitch
This is the timeless classic from the Father of Modern Chess. Nimzowitch was the first to explore and describe the game of chess from a viewpoint of its "elements." At the same time, he layed the foundation for modern positional play with his concept of overprotection This is required reading for anyone aspiring to mastership.
Title: Basic Chess Endings
Author: Reuben Fine
This is the Bible for chess endgames. Every conceivable endgame that could ever arise is analyzed by a superb GM. It will take you months, even years to read and understand this book. Although tedious work, your effort will be rewarded by this book. Only drawback: It's in descriptive notation. All other efforts since this endgame study have been basically to condense the knowledge in this book.
Title: 1001 Winning Chess Sacrifices And Combinations
Author: Fred Reinfeld
This is probably the most famous of the "tactical trainer" genre.
It is well known that tactics is the weakest part of an amateurs
game and prevents his progress. I do about 10 of these
exercises a day to keep me tactically "fit." A must for anybody
Title: How To Reassess Your Chess
Author: Jeremy Silman
This book is already considered a modern classic. You can think of it as a modern "My System," but in a more user-friendly presentation. It introduces the reader to a new vocabulary and concepts in much the same way. Tons of improving chessplayers swear by this book. It is a "I want results now!" book.
Title: My 60 Memorable Games
Author: Bobby Fischer
60 great games annotated thoroughly by arguably the best chessplayer in the history of the world. If you get any game
collection book, make it this one. You will spend many pleasurable hours by the chessboard playing over magnificent games, all fabulously commented.
Title: The Art Of Attack In Chess
Author: Vladimir Vukovic
A necessary component of any chessplayers library is this treatise by Vukovic on the subject of Attack. This book guides the reader through all the common ideas that are essential so that you can "bring home the victory." Aggressive players will love it.
Title: tZurich International Chess Tournament 1953
Author: David Bronstein
This tournament book stands out from all other books because of Bronstein.
Many strong masters of the day played at this tournament of lore:
Bronstein, Smyslov, Keres, Reshevsky, Petrosian, Geller, Najdorf, Kotov, Taimanov, Euwe and so many others. Bronstein studies all 210 games with great annotation and throws in stories as well.
Title: Logical Chess: Move By Move
Author: Irving Chernev
This book is incredible because it gives an explanation after every move! Everybody is tired of books that give a line and no annotation or explanation. Well, this book is the answer chessplayers were looking for.
Title: The Ideas Behind The Chess Openings
Author: Reuben Fine
Although the openings studied are often not up to date, that is not the
point. This is not a traditional openings book that may "teach" you
the Sicilian, it attempts to explain the WHY not the WHAT. In this
regard, it is similar to "Logial Chess: Move by Move." An
important classic so you can play the first moves with understanding
Title: Pawn Structure Chess
Author: Andrew Soltis
Books like these have become increasingly important in the information age. It is no longer possible to blow out your opponent in 15 moves every other game. Modern masters rely on their knowledge of topics such as pawn structures to separate them from the stronger amateurs. This book lets you know exactly what they know.