Play your Wii
The Wii U's backwards compatibility is somewhat different from what the other consoles do. It's more like putting your PC in MS DOS mode than simply sticking a PS2 game into your PS3. When you select the Wii channel on your Wii U, it boots up the system as if it was a Wii.
And by transferring the data from your old Wii onto the new Wii U (via an adorable Pikmin-themed loading screen), you can retain everything you had on your Wii, including game downloads, saves and more.