My very first game was Rayman 2: TGE for the N64, but I would have to say that the game which truly got me into "gaming" in general was... well I think I'll have to cite three to truly answer the question.
There was Halo: Combat Evolved, which was the first game I ever really played multiplayer with my friends. Then there was Halo 2, which was the first console/shooter game I ever played regularly online. On the PC front, there was Everquest, which was my first MMO. I played it when I was 8 with my dad, which inevitably led me to try World of Warcraft a few years later when it came out and I only finally put that to rest with little intention of returning several months ago.