Super Mario 64, in terms of modern game design, established a lot of golden rules that is still followed today. How players get motivated and how levels create player motivations and stuff like that, and the dynamic possibilities of 3D movement.
The original Mario Bros. made games fast, dynamic, and made game designers consider things like variation and power ups in a more meaningful way than before. As well as showing how important music and art styles are.
Doom's adult themes and visceral feedback influenced the entire industry overnight, it shaped PC gaming during the 90s, just like Mario Bros. did for console games. Of course, that game changed game tech forever as well.
Half-Life changed how we view set pieces and game direction, getting away from the "level to level" feel of other games, and used sound effects and clever tricks to manipulate the player in a more sophisticated way.
A lot of games like Ultima, Zelda, Tetris or Sim City has had massive influences, but it's more genre specific, but Mario (64 and original), Half-Life and Doom changed the industry completely. They changed how game designers view the medium. It's hard to pick one, but I think that's the big four in this discussion.