Wii remotes use bluetooth. So do PS3 controllers. Very nice because it means you can use them with a PC as long as someone has written drivers. MS went with a proprietary wireless protocol for their controllers, in order to lock out third-party manufacturers. That's why all the third-party gamepads for the 360 are wired (and yet still somehow
expensive as hell 
).
And nope, the newer versions (since Nov 2011) do not have Gamecube backward compatibility. The controller and memory card ports have been removed, and they won't play the discs. Becuase of the way they bundle/package things, though, you could still get new early-design Wiis for a while after the new design launched. It's easy to tell at-a-glance which one you're buying: the newer version is designed to be placed horizontally, so the button labels are located accordingly.
Pretty stupid if you ask me. I know cost-cutting was necessary to keep the "cheap family console" priced below the late-model PS3 and 360 redesigns. But even if you don't have Gamecube games to play this can hurt, as a lot of early third-party Classic Controller alternatives used the CGN controller ports.
Even worse is the new Wii Mini that seems to be Canada-exclusive. No Gamecube support, no SD card, no component (480p) video output, and NO NETWORK SUPPORT. Which means no virtual console or downloadable games. AND it's ugly and looks like an aborted NES 2 or Virtual Boy design from the 80s. $50 less than the regular (still GCN-free) version with half the (remaining) features cut.
