In no particular order
Virtual ConsoleWho doesn't want to be able to play classic games.
DS SupportThe possibilities are endless. Use the DS as a controller for the Wii or maybe simply as a secondary display device. Use the Wii as a gaming hub for the DS. You could download demos to the Wii that could be shared with the DS via Download Play. Use the DS to further explore worlds for a Wii game (maybe special levels you can only get to with the DS). I could keep going.
Backwards compatibility with GameCubeI would love to play all the Mario Parties that came out on the GameCube or my favorite the Prince of Persia series. The
Wavebird is a great wireless controller and would work as well.
Wii Remote and Nun-chuk controllerJust go watch any of the videos on You Tube to see just how awesome this controller is going to be.
WiiConnect24Finally, some true Internet loving from Nintendo.