Unfortunately, I kind of "missed out" on Nintendo consoles apart from the handhelds (all of which were Nintendo; GB, GBP, GBC, GBA SP), so I'd never got the chance to play the NES, SNES or N64. I used to play the GC and Wii at my friend's house, but we've drifted apart and stuff.
So I guess my favourite Nintendo system is the Game Boy Advance SP, probably the console that I play the most now and then and that I've had for the longest time without breaking. Also, backwards compatibility for Game Boy and Game Boy Colour games is pure win. And I actually got to experience SNES games like Super Mario World and the Donkey Kong Country series on a little portable that I could stop at any time, put in my pocket, and then just whip it out to play again.