1. Ms. Pac-Man
I refuse to pick just one of these (tied with Roadblasters), because they're important in the same way. Before we ever had a console in the house, I played these every time I went to my mom's workplace. I always felt like I got ripped off, somehow, but I kept going back to them.
(See Ms. Pac-Man.)
3. Bionic Commando
One of the first games I got when we became an NES family. (Mario/Duck Hunt and Skate Or Die! were the others.) I learned this game inside and out. It was the first game I ever mastered, and always wanted something similar. Didn't get that until 2008.
4. Super Mario Bros. 2
I always prefer that sequels to games be mechanically distinct, and not just an expansion. I didn't own it until I was in college, and had only played a copy at a friend's house (using an NES MAX if I remember correctly), and loved it. Couldn't articulate why until the industry became so heavy with rehashed sequels.
5. The Legend of Zelda: A Link to the Past
The first game we got for the SNES I won in a local store drawing. (Technically, a $200 gift certificate for toys, but come on, what else would I have gotten?) This game felt enormous then, and ever since, I've loved BIG games, even when their content and mechanics are nowhere near as polished as this.
6. Final Fantasy Legend II
The first portable RPG I ever played. Played this one in cars, church, the bus, at home, with friends, alone. My love for crazy-long DS games comes from here, I'm sure of it. (Love you, Etrian Odyssey!)
7. Gran Turismo
Got me to buy a Playstation and a Dual Shock to figure how to play it right, and was the earliest game I can remember as deeply customizable as it was. I'm not big on driving games, but all the little tweaks here informed my RPG tastes in a way I'll never forget. I'll say it like this - GT made me a better Final Fantasy Tactics player.
8. Half-Life: Counter-Strike
The first (and really only) game I ever meant to compete in. Started early (beta 3? Which one had the fast run w/knives out?), played HARD. Played on a ladder and went 9-0 with dudes from my dorm before the whole thing went belly-up that summer break. I've never played anything that gave me the camaraderie that this did, with anyone.
"You know, these songs are really catchy and crazy, and this tiny plastic guitar is ridiculous, but awesome. Someone at Konami needs to bring this to the US!" I'm nowhere near the "talent level" in GH/RB that I was in Guitar Freaks, but hot damn, this was sweet in college, especially since my actual guitar talent fell short of my ambitions.
10. Metal Gear Solid 2: Sons of Liberty
I think this is the first game for which I was actually a little crazy about "WHEN IS THIS COMING OUT". Also, there was a contest where you could try to get your name in the game. My friend Pawel is one of the earliest guards on the hardest difficulty, and I have shot him in the head and dumped his body overboard many, many times.
11. Shin Megami Tensei: Persona 3
The most recent game to get me really, really back into games. I'd had plenty of great experiences, sure, but this really hit a sweet spot for me. Shortly after this, I bought a PS3 because if stuff like THIS was happening on the aging PS2, what the hell am I missing out on? (Short action games, apparently. Oh well!)