I just perused my bookshelf and these were the essentials that jumped out:
"Chess Tactics for Advanced Players," by Averbakh. Shows the importance of the double attack and how it plays a key role in all successful attacks and counter-attacks.
"Chess Middlegame Planning," by Romanovsky. Shows the role for proper handling of the central stage of the game, as well as how to hatch a plan.
"Complete Chess Strategy Vol. I, II and III," by Pachman. Shows the first principles of the middle game, principles of pawn play and the center, and the endgame. A good all around primer on all three phases of the game.
"My Best Games of Chess," by Smyslov. Excellent analysis of high level games by a World Champion. Playing over Smyslov's games will teach you how to win a won game!
"Three Hundred Chess Games," by Tarrasch. A wonderful, instructional set of games played by Tarrasch. Chess players may enjoy playing through Tal's games, but they learn how to play the game properly by going through this book. Basically a distillation of the whole of chess knowledge through the Hypermodern era.
"Capablanca's Best Chess Endings," by Chernev. 60 of Capa's best endgames. I've gone through this book many a time and still continue to find instructional value and enjoyment from it. If I'm every planning to be stuck on a desert isle, this one is definitely going.
"Rook Endings," Levenfish and Smyslov. Rook endings occur in over 50 percent of endings. Master the material in this book and you greatly increase your winning percentage.
"The Tactics of the End-Games," Jeno Ban. This book is similar to the Averbakh book mentioned earlier. The author demonstrates the importance of the double attack in the end-game, as well as assorted other dirty tricks your opponent might not be considering. Think the end-game is dry and dull? Read this book and you'll never view the end-game the same again.
"Domination in 2,545 Endgame Studies," by G. Kasparyan. Every type of endgame tactic and situation is demonstrated with an encyclopedic 2,545 studies. Some examples: Trapping Minor Pieces, Trapping a Rook, Trapping the Queen, etc. Every great endgame composer is represented in this volume: J. Berger, Birnov, Bondarenko, Bron, J. Fritz, Gherbtsman, Gorghiyev, Gurvich, Halberstadt, B. Horowitz, Kling, Kubbel, M. and V. Platov, Prokes, Rinck, Troitsky and many, many others. This book is a tour-de-force of the endgame study.