Actually for me it started on Atari 2600. I got a game for x-mas called Mario Bros. And Donkey Kong. Not too long after the Atari I'd go to a friends house and play games like double dragon 2 and Contra (oh how I loved contra..up,up,down,down,left,right,left,right,B,A,select,start) and of course Super Mario Bros. was the game. Every house party the kids had an NES Mike Tyson's punch out, excite bike, I mean really the NES was THE system. Golden Cartridge...No need to say any more.
Then it was the SNES, my personal favorite. SMW, and oh man Donkey Kong Country (1&2) Chillin in a crib with my boys playing Super Street Fighter 2 tournament style ( I was a legend with Ryu) Super Metroid for my solo gaming, it was incredible. Mario RPG and Chrono Trigger oh shit I'm getting emotional lol. Link to the Past...No need to say any more.
N64..In some ways many of Nintendo's franchises have their best iterations on this console. Over all SNES is my favorite system. Followed closely by this one though. But this Console has my personal GOAT game..I'm sure you can guess which game it is..no, its not Golden Eye, Star Fox, Wave Race 64 (close) Mario 64, Mario Kart, AKI wrestling games (we still talk shit to this day about who's wwf champ in those games) Smash Bros. The commercial alone sold me on this one. Rogue Squadron needs mentioning... But..No it was Ocarina of Time. Gamings pinnacle for a 15 year old in New York. I was blown away by that game..ONE game comes close to giving me that feeling..But it wouldn't come out until 2007...
GC: let's see...they lost me, sort of with this one. The games all fell short to their N64 counterparts (IMO) With the exceptional game being Metroid Prime & RE4..REmake also must be mentioned that game looks stunning to this day. Wasn't feeling Melee as much as the original, HATED double dash..Eternal Darkness was cool, the Rogue Squadron games looked fantastic, but was missing that..special something..maybe because it only took 9months to make. The Swan song Twilight Princess was a good send off though..Better than that craptastic Wind Waker (sorry Khuutra lol).
Wii..Was going to pass up on gaming this round, felt it was becoming to stagnant and predictable. Every thing was just updated versions of N64 games but with added visuals. it wasn't until I was at a friends house and tried Wii Sports that I was sold..that and I became aware that a game starring a certain Bounty Hunter was dropping soon. So I invested in Metroid Prime 3..Holy Shit. To this day it is my favorite single player experience on the Wii (or any platform for that matter). Blew me away, it was fresh, looked fantastic, and was a full experience all the way through. Then there's Galaxy, Rebought RE4 (great investment) MK Wii, But the game for me: Brawl. I play this game daily it is the best MP game I've played since Golden Eye..In fact Wii to me has surpassed many of the N64 iterations. We'll see what Zelda does and hopefully there is a Star Fox game in the mix. NSMB is fantastic. So yeah,
All of these systems have shaped console gaming as we know it. Nintendo is a trailblazer, like em, love em, or hate em. There's respect there. Even the most die hard Sony, M$, and Sega (yes they still exist) fans can respect what Nintendo's brought to the gaming table.
But as for me, they are tied to my child hood and fond memories that go along with that. That's why I'm a fan. In addition to my own bias of liking the originators rather than the duplicators..I like Mike, not Kobe for example ; )