Comment Re:I'll wait and see (Score 1) 330
According to Marc Franklin, Nintendo of America's Director of Public Relations, it will not play GameCube games.
Link is down at the moment but this is where I got the news.
Yes, the Wii was based on GameCube architecture so it could theoretically still be possible. The Wii U does not have any GameCube controller ports or memory card slots so they would have to be provided via USB or Bluetooth and associated IO processing would have to performed. It's unknown as to whether or not the slot loading drive on the Wii U will accept the smaller GameCube discs or not.
Not to mention that Nintendo's backwards compatibility usually lasts only one generation. Look at Gameboy/Color games on the Gameboy Advance (gone on the DS) or Gameboy Advance games on the DS (gone on the DSi/3DS)
tl;dr - I wouldn't get your hopes up.