Morrowind, of course. Weirdly it was the XBox version I played first (at a friend's place), but that was a dog so I got it on our PC (GeForce 2, good times). I've got Morrowind and about two hundred mods installed even now, but I daren't play it because I know I won't be able to stop any time soon. No doubt I have sunk more hours into Morrowind than any other game ever.
The Legend of Zelda: Majora's Mask is another one. Have to love the world; it's like a surreal painting. It's also unique in that my mom approved of my playing it, although I'm not entirely sure why.
Also, the Pokémon games on various Game Boys and, to a lesser extent, the Nintendo 64. Think what you will of Pokémon - I do - but some of the games are genuinely good, others brilliant. There, I said it first. You can come out of you Pokémon closets now.
Games that I wouldn't count as life stealers but are still pretty important when it comes to my earlier years include Paper Mario, Jet Force Gemini, F-Zero GX, Metroid Prime, Super Smash Bros. Melee and Goldeneye.