You will often read in chess books that we should study the classics. Outside of World Championship games, it is not entirely clear what authors mean by that. Telling an amateur player to play through every played game by every elite player is neither a fun, nor a realistic plan for a player trying to become acquainted with famous ideas. Improving players have asked me countless times what the classics actually refers to, because there is not an actual list put out by any highly-esteemed chess authors, coaches, or top players. Players are essentially left to their own devices and we know what usually happens then: due to an overload of information and games to study (here, study this 3 book series on one player...), nothing gets studied at all. I put together this compact list of classic games to highlight the most useful ideas to be aware of. Most lists of classics are plagued by featuring too many surprising checkmates (that even modern 2200 players, let alone top Grandmasters, would very rarely fall for) that occur at the end of an otherwise not particularly instructive game. I balanced this list with positional ideas, defensive ideas, and more slow-moving attacks than just the usual double exclamation mark sacrifice and stock mate.
Useful plans to recall: Qa1 by Reti (game 7), d5 and Nd4-c6 by Reti (game 9), Qe3!! by Botvinnik (game 11), Bc5 by Alekhine (game 12), Be3 by Boleslavsky (game 17), Ba7!! by Karpov (game 29), and the king walk by Short in game 42. Additionally, games 8, 14, and 46 feature tremendous domination.
Great defensive play can be found in games 18, 19, 35, 37, 38, 39, and 40.
Lastly, take a look at the famous sacrifices of Qxe5!! by Gusev (14), Rxa1 by Bronstein (game 15), Ne5! by Botvinnik (game 16), Re6!! by Petrosian (game 19), Be6!! by Fischer (game 20), Rxf4!! by Nezhmetdinov (game 22), Nxf2!! (game 24) and Rf6!! (game 25) by Fischer, Rd5!! by Kasparov (game 31), f4! and Rxf5!! by Gufeld (game 32), dxe6!! by Polugaevsky (game 36), Nxf2!! by Zvjaginsev (game 50), Qg7!! by Ivanchuk (game 51), Bh3!! by Shirov (game 52), and Rxd4!! (game 53) and Rxc3 (game 54) by Kasparov.
Please note that no World Championship games are given on this list intentionally, because every player should have a basic familiarity with World Championship games. I made this list to give helpful direction to players not sure what the chess classics refers to. Nearly every game in this list features a particularly memorable plan or idea beyond the scope of just a stock checkmating pattern.
If you think any games belong on this list, please let me know which idea from your proposed game was particularly memorable and classic. While making this list, I looked through over 100 lists of games and numerous books, including one by Grandmaster Soltis and the games featured in the five My Great Predecessors books by Garry Kasparov. I have left out repeat ideas as far as possible (with the exception of the Qa1 plan).