It is very hard to choose but today i choose the Gamecube.
My kids were getting older and I got some play time on my own. We still had multiplayer blasts with Double Dash (even my wife joined in), Smash Bros (I sucked big time), Mario Party (that was intense) and Timesplitters (so much fun).
On my own I played two great Zelda games, my favourite Mario ( Sunshine), Factor 5 Star Wars games, RE4 Metroid Prime, Pikmin, Need for Speed, Super Monkey Ball, Tony Hawk, Viewtiful Joe, Eternal Darkness, Chibi-Robo, LOTR:tRoftK, Wave Race, Beyond Good and Evil.
I watched as my oldest son played Killer 7,Fire Emblem and Ikaruga (with the CRT TV turned sideways),
It has the games I probably played the most ever: Animal Crossing (with Freeloader because I bought the NTSC version), Fire Emblem Path of Radiance (thanks to my oldest son), Paper Mario TTYD and Smuggler's Run.
It was such a good system that I totally missed out on Luigi's Mansion, Star Fox, Tales of Symphonia, F-Zero and other games.
After that it was X360 for some years and I did not play much for a couple of years (except Vikings: Battle for Asgard).
But another day I might choose another console as my favourite!
