Hmm...
First Game: Super Mario Bros. for the NES
I figure that my discovery of this game at around 3 years old, and the next two to three years I spent learning how to operate the NES were what got me started. That's only half of it though.
Game that got me hooked: Star Wars X-Wing / Star Wars Jedi Knight: Mysteries of the Sith (Demo)
When I was 5-7 years old, I bugged my parents until they bought me a Star Wars collector's box set of games because it had TIE fighters on it and I wanted all the Star Wars I could find. We took it home, and I installed all the games on my windows 93 computer. Star Wars X-Wing, TIE Fighter, Dark Forces, XvT Flight School and demos of Dark Forces II and Mysteries of the Sith were included. These were my first real taste of gaming, and I played these until something like 2003. Unfortunately, flight sims died well before I was ever old enough to buy any of them, so my skill and love for flying X-Wings goes unrequited. I've found numerous small mods and short indie games, but nothing matches a full release of a new X-Wing game.
I am a gamer today largely because games and Star Wars collided in the 90s, and I hold out hope that someday LucasArts will stop making those horrible Force Unleashed games and release more BattleFront games on consoles and PC. Or that they'll add another entry to the X-Wing or Jedi Knight series, whichever comes first.