Street Fighter II, as it's hard to deny how influential that was in the early nineties. To this day, the formula has not been improved upon (by much).
Mario 64, don't want to explain this one too much, it's was a perfect game at the time and a template for how 3D polygonal games should be like for years to come.
Quake, I know Doom is already in the Hall of Fame, but Quake was the first truly 3D first person shooter and basically ignited the online multiplayer craze (Doom was IPX LAN only). To this day there's leftover quake netcode in games like CoD and the Source games. It made WASD + mouse control viable (wasn't really needed before) in FPS games, which is still the optimal control scheme today. It made modding mainstream (wasn't the first moddable game, but it was the first truly mainstream at the time).
Super Mario Kart, it was the perfect multiplayer game and spawned a very good franchise, not to mention all manner of clones. But the main reason I'd have this in the Hall of Fame is it's impeccable gameplay, which allowed for an almost zen-like mastery at the highest levels of play.
There's just so many other games that deserve it too, I hope they don't limit the number of entries to retain a feeling of exclusivity. I want Half-Life in there, I want Counter-Strike, Unreal Tournament, Gran Turismo, Virtua Fighter and Tekken, Supreme Commander (the first one), Command & Conquer, and so on, and on, and on ...