I'm not sure. It might have been Tetris or Pac-Man, Space Invaders, I dunno.
First one I absolutely cement as a gaming memory is Stonekeep for DOS systems (I have an extremely bad memory of some of my early years, so this is skipping forward quite a bit). Legendary game, I think it might be abandonware now, so pick it up and try running it on DOSbox.
Hell, I'm gonna go through my first game for every system I've played, and why the hell not. Again, largely cut ause of my twice-damned memory capabilities.
DOS: Stonekeep.
Dreamcast: The Floigan Brothers. This may be either a famous game or an underappreciated shining gem, but I love it.
N64: Super Smash Brothers.
Windows: The Secret Of Monkey Island.
PS2: James Bond: Nightfire. A local multiplayer classic. Seriously, I don't think I ever played Goldeneye's multiplayer, but this one was probably it's equal if not better in that department.
Original Xbox: Halo: Combat Evolved, which I played at a friend's after hearing great things about it, which, at the time, involved GamesMaster magazine as the sole bearer of gaming news.
GameCube: Metroid Prime. I wept many tears during the slow death of the GameCube. Not as many as for the Dreamcast mind.
Xbox 360: Halo 3. Don't listen to the haters, this is a multiplayer extravaganza, and it's infamous community of swearing 9-year olds lends proof to the Rebel748 Multiplayer theory (Not the same as the Greater Internet Fuckwad Theory): Multiplayer is always better in local splitscreen play or a LAN environment. Always, and with no exceptions.
PS3: LittleBigPlanet. A personal favourite.
That's all I can think of. Here's to unneseccarily long posts!