Good question. Here's what I think most influenced me.
1. Baldur's Gate. Back in early high school, I thought computer games were kind of lame. I was big into pencil & paper roleplaying games, though, so when a friend told me there was a computer-based D&D game I had to try...well, I was sold. After that, I ended up playing a ton of similar games, and I have no doubt that BG shaped a lot of my gaming preferences. (Just look at my word cloud, for goodness' sake.)
2. Final Fantasy VII. This was the first time I really got hyped up for a game before it came out. It was also the first time I bought a strategy guide. Basically, FFVII was my first true console experience -- I had played a lot of games on the NES and Sega Genesis, but only with (what we would now call) a casual approach. FFVII changed all that.
3. World of Warcraft. This one is kind of odd, because I really hate WoW. I could probably log on at any time and spend a full 24 hours playing it, but I absolutely hate it. Why was it such an influence on me? It made me realize that there is a lot more to a good game than addictive gameplay. It also made me extremely reticent to try any further MMOs...
4. Longest Journey. I had always thought adventure games were lame before playing Longest Journey. It really opened my eyes, which is a good thing, because lots of good adventure games have been coming out in the past couple of years.
5. Neverwinter Nights. Ok, so this game was in many respects as important to me as BG was, but with one major difference. NWN had (has?!) an incredible community of modders that were always adding new stuff to the game. I played it for at least two years straight, and it isn't an MMO! This one made me start paying attention to whether or not games included modding utilities.