The first computer that I played games on were the one that my dad wrote his thesis on. I don't know what kind of computer it was but I played pacman clones, commander keen, cosmos cosmic adventure, crystal caves, secret agent, Bio Menace and Wolfenstein 3D. Probably a lot more games as well that I simply don't remember.
Later on I somehow got a snes (I honestly have no idea why or when and have never asked) and that was co-op heaven for me and my friend. We played Legend, Super Mario World, The lost Vikings, Street racer, Turtles in Time and Mortal Combat. All good fun.
Even later on I got a decent computer and started playing games like BG1 and later 2, Diablo 2 and especially Heroes of Might and Magic 2. I'm saying especially here because it would lead to my friend getting HoMM 3 which lead to us becoming crazy about that game and playing it in hotseat mode. Many weekends were wasted doing just that.
I would then over the next few years get interested in gaming as a hobby more and more, part of which was getting acquainted with the internet and through that Fallout (which I had owned for some time as a free game from a gaming magazine) and then fallout 2 and PS:T later on. I actually have a memory of starting up fallout much earlier in my life and being beaten to death by molerats shortly after leaving vault 13. I didn't play anymore after that.
I only started getting back to consoles in this generation with the 360.