Hm, that's a tough one.
It was probably Super Mario Bros on the NES, since I got the system and a few games (Mario, North vs. South, Ghosts and Goblins) from my mom's cousin after he got himself a SNES. However, it might potentially have been Wario Land: Super Mario Land 3 on the Game Boy.
However, the first game I played that really got me hooked was Age of Empires 1. I sunk endless amounts of hours into that game.