These are often books about chess tournaments or chess championships, or the best games of individual players. I am only recommending my favorites. Use the links to check out what others have said about these books at Amazon.
Please note that only the first of these would be helpful for children or absolute beginners (and, unfortunately, it is out of print and expensive). Still, the fastest way to improve? To play through game collections just like these!
1000 Best Short Games of Chess, Irving Chernev. A new edition of this classic will hopefully soon make it affordable for the young generation. We tell young players to play through games to improve, and these are short works of art to enjoy.
Tal-Botvinnik, 1960, Mikhail Tal. This is, perhaps, the best chess book ever written. The games are wonderful. Tal's notes are full of energy and enthusiasm. All of the games are from the 1960 World Championship match in which the younger Tal defeated the long standing champion.
Here are the games from Tal - Botvinnik, 1960. A convincing win for the tactical Tal Crosstable
Chess Brilliancy: 300 Historic Games from the Masters, Iakov Damsky. A dazzling collection of great games from 1968-1998, all from the recommendations of the best games in the yearly Chess Informants. All of the games have been subjected to a lengthy, computer-based analysis.
100 Selected Games, Mikhail Botvinnik. At Chess is Fun, you will find many of M. Botvinnik's World Championship games. Here are his favorites, with wonderful annotations. Don't miss his first brilliancy prize against Tartakover at Nottingham.
The games from "100 Selected Games"
Chess Highlights of the 20th Century, Graham Burgess. The best games and most exciting positions organized chronologically, giving the reader a large dose of great chess and well-written history. Includes photos of the great players.
The Chess Analyst, Jon Edwards. I admit that my book doesn't really belong in this list of chess greats, but I hope that you give this book a shot. It's NOT for beginners, but I put a lot of tender loving care into this. The link takes you a special page that has all of the games available for free!
The games in "The Chess Analyst"
Software Game Collections
Bobby Fischer. GM Robert Hübner has thoroughly examined Fischer's biggest and best known publication, "My Sixty Memorable Games". This ChessBase monography includes reports on Fischer's most important chess matches, including contemporary material.
William Steinitz. More than 1,000 games, 42 texts, database with training questions, and more...
Mikhail Tal. Collection of all 2857 games of Mikhail Tal with biographic texts and pictures and video. Historic Videos.
Correspondence Chess Database 2002. A comprehensive collection of correspondence chess games, including a few og my own. These games tend to be very well played and often involve interesting theoretical battles
Emanuel Lasker. A close look at Lasker's chess - extensive game collections with annotations, multimedia, and much more.
Jose Capablanca. 640 commented games played by the 3rd World Champion Jose Raul Capablanca. All the games deeply annotated by GMs Khailfman and Petersburg IMs.
Emanuel Lasker. The most complete collection of Emanuel Lasker's games ever compiled. Contains 630 games, covering the entire long career of the 2nd World Champion.
Alexander Alekhine. "The chess games of Alekhine - one of the foremost chess artists of the past - will live on for centuries. Chess players will always enjoy playing over Alekhine's games and marvel at his genius". (M. Botvinnik, The 6th World Champion)
Master Chess Game Collection. 1.4 Million games dating from 1485 to August 2002. MasterChess 3000 is an inexpensive yet powerful chess database & playing program. It comes with lots of easy to use features and most important, it's affordable.