NES
Wasn't born when it came out. However, I have played most of the great NES games through the NES classic series (on the GBA), through the numerous ports and remakes and I played a few NES games through Animal Crossing on the GC.
Game Boy
My sisters had a Gameboy ever since it came out. I constantly played Mario Land and Tetris on it when I was young and loved it. This handheld was what got me interested in Nintendo.
SNES
When I was about 5 (may have been 6 could of even been 7. God knows. It will remain an eternal mystery. It might have even been 8. Actually 8 sounds a bit too old. 5 or 6 sounds sensible to me) my parents got me a Sega Mega Drive, and therefore didn't have SNES. Back then though I was too young to even know about the SNES. I loved the Mega Drive a lot, I owned all the Sonic games and played them to death. I also loved games for it such as Streets of Rage and Golden Axe. Eventually though I brought a SNES with games such as Mario All stars and Mario Kart, and loved that too.
Gameboy Pocket
My Sister brought one of these. This wasn't really a big console for me. I just played on the old original GameBoy.
Gameboy Colour
This was a big handheld for me. I got one of these for my birthday (please don't ask me which one. OK? Else this could turn into an even longer post) with Wario Land 2. Wario Land 2 was a game loved a lot. Also I was introduced to the Pokemon franchise, so I got Pokemon Yellow for my birthday followed by Silver (when it came out in America- yeah I imported it) and then Crystal (once that was released in America- indeed, I imported it). On this handheld I caught up with a lot of games I missed out on on the original Gameboy (mainly Mario ones

).
Nintendo 64
It was either this, or a Dreamcast. Mario, or Sonic? Last Christmas my parents brought a Playstation as a family present. With my love of Pokemon I decided to buy a Pikachu N64 with Pokemon Snap. I loved this console a lot more than the Playstation, with games such as Mario 64, Smash Bros and Lylat Wars it was one of my favorite consoles.
Gamecube
This is where I beleive I became a real Nintendo fan. Before this console I wasn't really interested in games other than Mario, Pokemon and DK games. But now I was older I started to become interested in other Nintendo series such as Zelda, Metroid , Fire Emblem and F-Zero. With my new found interest in other Nintendo games I went back and brought games I missed out on on the Gameboy series, SNES and N64 (eg: Goldeneye). By the way I own all the Metroid, Starfox and Zelda games.
Gameboy Advance
Of course being a big fan of the Gameboy series I got this handheld. Of course, being a Mario fan I got Mario Advance, Wario Land 4 and Mario Kart Super Circuit with my GBA. I caught up with the games I missed on the NES (such as LOZ ,LOZ 2: AOL and Metroid) through the numerous ports and remakes and also through the NES Classic series. I also caught up with the SNES games I missed out (such as LOZ: ALTTP and Donkey Kong Country 2) on through the numerous ports and remakes. Now a fan of games such as Metroid, Fire Emblem, Zelda and F-Zero I brought many GBA games. I also got this so I could play my old GB and GBA games on it.
Gameboy Advance SP
I was sick of not being able to play my GBA in the dark and not being able to see the screen properly most of the time, so I got this.
DS
I don't really need to explain why I got one of these. It has all the games I like on this console so its literally perfect for me.
DS Lite
I broke my old DS so I got one of these, and I love it. The thing that let the old DS down was the fact it was fat and ugly. This however has a perfect design. Great games+great design+innovation=perfect console.