Here's mine:

10. The Wii. Way to bring back middle-aged parents into gaming, Nintendo.
9. Mario 64. The true birth of good 3D gaming on consoles.
8. Pokemon. Why are all these kids excited? Dunno, just buy them this shit to make them shut up.
7. Gran Turismo/MGS/FF VII. The triumvirate that brought disc play into popularity and brought in the masses through great gameplay.
6. Sonic II. There's another player and they're called Sega. They have a mascot that just might kick Mario's ass.
5. Halo 2. Online console gaming is born. Hallelujah.
4. GTA III. A new genre is born and casuals grip on again.
3. Super Mario Bros. Gaming has a rebirth and that rebirth is brilliant.
2. Atari 2600/Pong/Pacman. Arcade gaming is brought home and people never stopped playing.
1. The NES. Simply put, it's the best gaming system to ever walk the Earth and it sold like gangbusters.

Damn, I just noticed this was "killer apps" not "great influences on gaming".

Still, Pong and/or Pacman being left off either shows the OPs age or his lack of gaming history. I think it's probably age. I'm one of the few codgers on this board that still remembers the 2600 when its main competition was Collecovision or Intellivision.

Gran Turismo for sure is one.
I think I have considering to buy a PS after playing GT with a friend.
For European country it was a must have.

 That's why I included FFVII/MGS/GT in my list. I don't think that any game on its own would have made the Playstation great but all three combined to make it a dominant force. They also released together in a rather short period of time considering how great they are.