Gamecube, because it's the console (I felt ) they were more experimental with and it had one of the best controller.

SNES is my favorite. But NES is a near-tie and in some ways superior. NES was just so ground-breaking and titles like Zelda and SMB and Metroid were so fresh, and Contra and Lifeforce and so many others just so fun. And video games were new and mysterious.

But the SNES content was just simply better and the games so much better produced. The RPG genre also really hit its stride.

No contest: NES. It's the system that made me fall in love with video games.

SNES is a close second, as it had some genuinely AMAZING games, and was THE system to own for great rpgs (still is, in my opinion). But NES just had so much going for it. So many great games, so many great franchises either started or made popular on it, with just a few examples being:

Super Mario Bros., Zelda, Metroid, Kirby, Tetris, Dr. Mario, Kid Icarus, Excite Bike, Punch Out, Star Tropics, Yoshi, Mega Man, Castlevania, Ninja Gaiden, Double Dragon, TMNT, Adventure Island, Bomberman, Final Fantasy, Dragon Warrior (Quest), RC Pro AM, Micro Machines, Battletoads, Contra, Wizards & Warriors, R-Type, Bubble Bobble, Joe & Mac, Duck Tales, etc. etc.

And that's to say nothing for great one-offs and quirky titles like: Crystalis, Conquest of Crystal Palace, Monster Party, Totally Rad, Kickmaster, Shatterhand, Metal Storm, River City Ransom, Kid Niki, Faxanadu, Power Blade, Shadow of the Ninja, Rad Racer, Mach Rider, Ice Climber, Bucky O'Hare, Monster in my Pocket, Super Spy Hunter, etc.

The best, in my opinion, is SNES. But my personal favorite is N64.

It was relatively weak in terms of fighters and RPGs, but it more than made up for it with a great collection of platform, action-adventure, racing, and shooting games. 

It would be hard to find a system with a better roster of 3D platform games. There's Super Mario 64, arguably the best ever made, plus Banjo-Kazooie, Banjo-Tooie (years ahead of its time), Conker's Bad Fur Day, Donkey Kong 64, and Rayman 2. For shooters, there's GoldenEye 007, which proved the viability of first-person shooting games on home consoles, plus Perfect Dark, the Turok series, Jet Force Gemini, Rogue Squadron, Star Fox 64, and Sin & Punishment. In the action-adventure category there's Majora's Mask, Body Harvest, Resident Evil 2, and Ocarina of Time, arguably the best game ever made. Finally, under the racing banner, there's Mario Kart 64, Diddy Kong Racing, Wipeout 64, Extreme-G, F-Zero X, and World Driver Championship.

The high quality and replay value of these games, among others, plus Nintendo's commitment to four-player multiplayer, earn N64 the crown.

The N64.

That system has the best games in almost each franchise. Plus you had amazing 2nd party games in especially Rare.
N64 > SNES > NES > Wii > GC. WiiU is yet to be decided, but it looks like it will at the very least beat the mediocre GameCube if they deliver on WiiU's Zelda. In handhelds it's a close race between the GameBoy (Color) and 3DS for me. I'd say GB(C) > 3DS > DS > GBA.

Gamecube. The last time they gave us a powerful console and just plain focused on games. Wind Waker, Pikmin, Pikmin 2, Metroid Prime, Metroid Prime 2, Double Dash, Super Mario Sunshine, Eternal Darkness, Luigi's Mansion, Animal Crossing, the list goes on and on. There's never been a system with so many games on it that I loved so much and I'm almost certain there never will be again. That generation ended almost a decade ago and I'm still going back and playing those games on a regular basis.

Just out of curiosity, was GC your first console? Just asking, because it seems like a lot of people most fondly remember their first system.

Nope, that would be my Sega Genesis.  Gamecube was just straight up magic for me!

My favorite Nintendo console is the 'Cube. Best Zeldas, Metroid, Tales of Symphonia, Capcom's games.

After the 'Cube:
2. SNES - probably Nintendo's most well-rounded library on a console.
3. Wii - Came out with some good "core" games like Xenoblade, Last Story, and Fire Emblem in the sea of casual stuff. I also loved Punch-Out!!
4. Nintendo 64 - It had my favorite Mario and two good Zeldas, plus a few little gems here and there.
5. NES - I only really got to experience the NES for about two years, then I went all PC for a few years before I got a SNES. Kind of hard to go back to the NES after playing SNES.

N64 easily
First steps into 3D was just an amazing thing.
OOT changed my life. Mario 64 was like babysteps after I played OOT