My favorite console at the time of its release and during its generation is different then my favorite Nintendo console of all time!
During its generation GameCube was my favorite platform. It had games from every one of Nintendo's main franchises and for the first and last time in history had games made by Nintendo Canada which really had me patriotically happy. I owned 35 first party titles for my GameCube and that was a major feat. In my opinion the GameCube had the best of all worlds, it even had Final Fantasy which hadn't been seen since the SNES.
Some will wonder why I never chose the SNES. When I was growing up I loved my SNES. But I only really bought three franchises Mario , Donkey Kong and StarFox. Other then those franchises and a couple great third party titles the SNES just lacked that all round feel. The GameCube had titles from all three of my favorite franchises and more.
Now my favorite Nintendo platform of all time has to be the Wii. But it has a massive unfair advantage. GameCube backwards compatability and Virtual Console. I can buy all of the games that I enjoyed on past platforms as well as any of the new games which aren't really the best in my opinion.
But as I said if you take backwards compatability and VC out of the picture my favorite Nintendo console is GameCube!