2-D is too generic. That's like saying name the best 3-D game ever. Every game used to be 2-D like 98% of all games now are 3-D.
- Platformer: Yoshi's Island
- RPG: Final Fantasy II (US FF II)
- Action game: Castlevania, the original one.
- Shooter: Xevious
- Puzzler: Tetris
- Sports: EA NHL series, the 16 bit NHL's were better hockey games than the Maddens were football games.
- Racing: Outrun
- Maze chase: Ms. Pac Man
If you're going to take one game out of the thousands of 2-D games ever made the answer is simple.
Tetris, no other game is as widely accepted, sold, played, recognized etc. than Tetris. It is what every "major" game with high production values, budgets, marketing and the like will never be... an icon playable by any age, race or culture. You can give Tetris to any person on Earth and they "get" it the second it's picked up. When Satoru Iwata talks about simplicity in game play? When he wants more games to be enjoyed by people? He wants the next Tetris.
Unfortunately the marketplace now has probably shot down the "next" Tetris as a design document. I don't think any publisher on Earth will come close to such an iconic game in the next decade.