John Harper in his blog says that the best way to understand gaming theory is to play these games. It's a list that heavily loaded towards indie games and so I own almost all of them (all but one in this list). However there are a few I've not yet played (in italics). I would add GUMSHOE to this list as it does things that no other game does whereas I'm not sure you need so many indie games. And what about Rocky & Bullwinkle or Dallas? Groundbreaking in their time. It's a list that is short on history (or geography, all the games are American bar one or two).
My Life with Master Primetime Adventures Sorcerer + Dictionary of Mu Trollbabe Dogs in the Vineyard Burning Wheel or Mouse Guard Poison'd Inspectres 1001 Nights Contenders Dust Devils Nine Worlds Capes The Shadow of Yesterday Shooting the Moon In a Wicked Age... Steal Away Jordan Swords & Wizardry or Labyrinth Lord, etc. D&D 4e and/or Warhammer 3e Savage Worlds Vampire (any) Call of Cthulhu Everway Over the Edge Universalis Grey Ranks Geiger Counter Danger Patrol Polaris HERO System Shock: Spirit of the Century 3:16 Apocalypse World