The game that got me in to gaming was actually the first game I ever played: Pokemon Stadium for the N64.
Yeah it may not sound like a big deal, but I was only about 5 years old and this was the first time I had ever come in contact with a video game. It wasn't actually mine, my parents were visiting some old friends of theirs and someone in their family had the console. They basically just plonked me in front of the thing to keep me entertained for a while, I didn't move from that spot for hours.
I was just amazed at how I could get these really cool looking monsters, (some of which looked like dinosaurs, which at the time were the standard of 'coolness' by which I judged pratctically everything) to breathe fire, create tidal waves and to hack at each other with the blades they had instead of arms.
After that I was hooked and when I saw a Game Boy Colour in a store I begged my dad to buy it for me along with a copy of Pokemon Yellow.
To this day I still have that hand held and game, I also wish that I could remember the face and/or name of the person who asked me if I wanted to play on his new console.