I am old school so I am going with SNES! A Link to the Past and Super Mario World are amazing! N64 would be #1 for me if I liked ANY game it had other than Ocarina of Time. Love my 3DS though since I can play my old school games on it too!
N64 is my favorite, and Gamecube a close second. The N64 had legendary titles (many of which are my top favorite games), and it really marks a time where a lot of experimentation and passion was put into game design. Nintendo took risks with changing things up, and it worked like a dream. Same for the Gamecube, but the N64 will always have a special place in my heart. I really could go on for hours talking about them both.
I also consider the Gameboy Advance SP a fantastic handheld. It can play Gameboy and Gameboy Advance titles (so you have a range from games as old as Kirby's Dreamland to much newer titles like Harvest Moon: Friends of Mineral Town), the backlight is pretty decent compared to its predecessors, and it holds its charge well. Though sometimes I wish I could find my old Gameboy, just for the sake of a good throwback. I was basically raised on Nintendo, so their consoles will always be my favorites.
The GameCube had the best games, and the Wii was the final "real" console Nintendo ever made, without all the Network IDs and Miiverse rubbish they have now.
ORIGINAL GameBoy, babies! It was the first device I got, including the so famous Tetris, version from '86! Gosh, how fond I am of that old grey brick...