I've been into games for as long as I could remember, we had a NES, a Genesis, and a Playstation when I was very young, and I remember I would play games like Spyro, Super Mario Brothers 3, Sonic the Hedgehog, Mortal Kombat, Punch Out, etc, etc. I remember that the first game I had ever played was Quake on the PC, and we had quite a few other PC games also, such as DOOM, Duke Nukem 3d, Jazz Jackrabbit, Sam & Max: Hit the Road, Full Throttle, etc.
I would have to say though, that the game that really "got" me into gaming, and cemented gaming as a life long passion for me, would have to be Grand Theft Auto: Vice City. Looking back, this was a horrible game to give to a 8 year-old kid, but I really loved it, being able to drive around the city, shoot random people, and all the explosions. All the possibilities in that game made me realize just how fun games could be.