Some Wii have Gamecube Support... I'll break it down by model.
The original Wii (RVL-001) DOES have Gamecube support, as it's compatible with virtually everything with the Gamecube... except the system add-ons (like the Game Boy Player). HOWEVER, it's virtually impossible to find these in stores (with a possible exception in the used section of Gamestop).
The newer "Wii Minus" (RVL-101) DOES NOT have any Gamecube support. It was removed to reduce the production costs for the Wii. These are what you'll find in stores nowadays.
The just released "Wii Mini" (RVL-201) DOES NOT have any Gamecube support... or any online support at all. This model is only available in Canada at the moment.
If you have an original Wii (RVL-001), you can play Gamecube games on it, but you will need a Gamecube controller & a Gamecube Memory card since all non-Gamecube stuff will be disabled when you enter "Gamecube Mode" on the Wii. The only way to leave Gamecube Mode is to manually turn your Wii Off (as you can't use the Wiimote to turn it off remotely).
The list of available Zelda titles on the Wii is as follows:
* Legend of Zelda (NES VC)
* Legend of Zelda II: Adventures of Link (NES VC)
* Legend of Zelda: A Link to the Past (SNES VC)
* Legend of Zelda: Ocarina of Time (N64 VC)
* Legend of Zelda: Majora's Mask (N64 VC)
* Legend of Zelda: Wind Waker (GCN)
* Legend of Zelda: Twilight Princess (Wii / GCN)
* Legend of Zelda: Skyward Sword
If you have a Wii Minus system, you lose access to Wind Waker.
If you have a Wii Mini system, you lose access to all those games except Twilight Princess & Skyward Sword.
Hope this helps!