Crash Bandicoot 1 was my first game... it was such an amazing. I looked at the most recent Crash Bandicoot games, and died a little inside. They are so terrible. I hope Naught Dog gets Crash Bandicoot back.
Going old school on ya, the first game I remember playing was Hunt the Wumpus on the TI-99/4A. I went from that to playing some of the Atari 2600 games that my dad had lying around as well as some games on the PC that my grandfather had that were on 8 inch floppy disks. After that I made the jump to the NES around 1988 or 1989. All these experiences happened very quickly one after the other as I quickly became aware of the joys that games could bring and it's been game-on ever since. Man, feels like I've been gaming since I was a fetus.
I had the Sega Game Gear. For those too young to remember this, it was basicly a bigger Game Boy advance. I had Sonic 2 and a basebal game. Then my first multiplayer game was Mortal Kombat 2. I'm living proof that violent video games don't turn you into a psycho.
The game that is engraved into my memory from my childhood is Banjo Kazooie for the Nintendo 64. That game just looked so amazing and had these giant levels to explore and get jiggies. Due to the limitations of being child I never fully completed the game but I'm considering getting the re-release on the Xbox 360.
When I go back and look, there was never one game that made me the way I am. I just was. Back before I knew there were other people who loved these games as much as I did. I always took chances I had to play any game I could. Hexen was a good one. Doom doom 2. Pokemon. Power rangers for the snes. Msortal combat, spyro. Wrestling games. Diddy Kong racing. Mega man x. You name it I either played it or wanted to. Its just how I was. Even when I was little I have pictures of my dad picking me up higher so I could see the pac man machine. Even now I can't go into an Laundromat without playing what ever game they have in there.