My favorite would have to be a tie between the ps2, ps3 and Gamecube.
The ps2 simply because of the huge amount of amazing games I played on it and the memories I have of it. The years I played the ps2 I was young and didn't judge games based on some objective "quality" fed to me by game journalists and reviewers. Some of my favorite gaming memories are of playing the old DBZ games and Rumble Racing with my buds.
The ps3 because it was the console that introduced me to online gaming. That opened up a whole new world for me. Hundreds of hours spent playing CoD 4 and sports games online, making tons of friends along the way. One guy I played CoD 4 with in 2007 I'm still friends with now.
The GameCube because, again, of all the memories I have with it. Countless hours playing Mario Kart Double Dash, SSB: Melee, Kirby Air Ride.
Now I mainly play games on my computer, unless I have friends over. I hope I'm wrong, but I don't think any gaming console in the future will ever give me experiences or memories like those 3 did.