When I was 3 my parents bought a NES for my sister. She liked it, but she wasn't alone... Eheh. According to my parents, I played with it more than she did. Although games like Zelda and Final Fantasy were far too complicated for me, I still enjoyed playing the original Super Mario Bros., Donkey Kong and of course the brilliant Super Mario Bros. 3!
A few years later my parents gave the NES away to some other family. I sill don't understand why they did such a thing. Nothing I can do about it now, though.
Due to constant whining on my part, my parents finally bought a SNES. I nearly fainted when I first laid my eyes on Super Mario World. It was amazing, I've played that game so much I think I might've finished it a dozen times, seriously
Although my father didn't like video games all that much, he loved Donkey Kong Country. I remember when my dad and I used to play that game. He never played console games later though... A few important titles I've played were Super Mario World, Super Mario All-Stars, Donkey Kong Country, Star Wing (Star Fox) and most importantly Zelda: A Link to the Past! My parents rented that game once, I was immediately sold. Since I had never played the original on the NES, this was something completely new for me. I never did finish it at the time, but it was the first Zelda game I had ever played.
Another few years later the N64 was announced, again I started begging for one (the tactic never fails :P). I was forced to sell my SNES with all my games, but I guess it didn't matter that much for me at the time. I still often regret it though...
Super Mario 64 was the first real 3D game I had ever played, both me, my parents, and all of my friends thought it looked amazing. Well it did at the time: "Look, Mario's blinking with his eyes!" Eheh, good times XD
Ocarina of Time, Lylat Wars (Star Fox 64 for all you Americans), Mario Kart 64, Goldeneye, Majora's Mask, Paper Mario. All great games form that era.
The Gamecube era was alright in my opinion, I got one for my birthday. Since I finally got a job in that era, I bought a lot of games. My first game was Super Mario Sunshine. It looked a lot like Super Mario 64 (gameplay wise), but I still liked it. A few important titles for me were the Wind Waker, Twilight Princess, Mario Kart DD, Timesplitters and a few more. My mind's kinda foggy, maybe I'll add some more later This era was a bit disappointing, although the fact that I was a bit older also might have something to do about it.
I recently bought a Wii, and I have to say that I really like it. The Virtual Console is a great feature and the games are getting some originality again. The future looks promising
I never really was much of a handheld gamer, the only portable systems I've owned are the GBA, DS and the PSP. I later on brought a "BrickBoy" for some amusement. But I prefer consoles for some reason...
All and all I think that the N64 era was the greatest. I loved Super Mario 64 and the Zelda games. I also played loads of multiplayer games like Perfect Dark.
Oops, wall of text