You can get all your Wii data over to your Wii U, but it's quite a process...
Nintendo promised that the Wii U would have backwards compatibility with the Wii, though the developer never really gave much in the way of details regarding how it would all work.
With Wii U review units sent out to major gaming media outlets, it's become clear that while the Wii U may have backwards compatibility with the Wii, it won't be an easy process to play Wii games on the Wii U. Not too long ago, it was revealed that Wii games on the Wii U wouldn't work properly with the Wii U Pro Controllers and would require the Wii Classic Pro Controllers.
Joystiq, after receiving its review unit, detailed the process of taking Wii data over to the Wii U. Essentially, a SD card must first be inserted to the Wii U, which must be connected to the Internet, and then the system transfer option must be selected on the Wii U. The SD card is then transferred over to the Wii, which also must be connected to the Internet. A "transfer application" needs to be downloaded from the Wii Shop to transfer all of the Wii's data over to the Wii U and wipe it from the Wii.
Though it's not too confusing of a process, it certainly seems like getting Wii games to the Wii U and transferring data might be a bit of a hassle.