PC: Either DOOM, Heretic, or Quake. Though my favorite childhood game was Toontown Online. Handheld: The Legend of Zelda: Four Swords. I got that, plus Frogger and Donkey Kong Country (GB version) for my 7-8th birthday, I believe? Console: I could never afford one growing up, and I can't remember what my first game was, but let's just go with Bioshock.
The first game I ever played was Jak II Renegade on PS2. Man, it's been so many years but I still remember how I sucked. I kept running and driving into walls. Good times, good times. Basicly I just screwed everything up. But I kept going on, and nowadays I could play through the game with my eyes closed. It's still one of my favourite games of all time.