Oh, man. Uhhhh.... I think it was the first Spiderman game for PS2. Oh god, that brings back memories. I remember I was on the last level and then suddenly I failed. I started playing the next day and I, for some reason, had lost every bit of progress. I raged so hard, the next county could feel my body heat.
Legend of Zelda: A Link to the Past, back on the SNES. Not that I was very good at it, being all of 3 years old. I'd steal mom's controller and just go about killing Link in imaginative ways all over the screen. That probably counts as playing, right?
The first game I played, in complete seriousness, was probably Tetris on the old Gameboy.