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While the Wii U is backwards compatible with Wii games, it is not backwards compatible out of the box. A firmware update adds Miiverse, the Internet Browser, and the ability to play Wii games.
Wii games cannot be run from the Wii U menu either. You have to turn on the Wii channel before you can play Sin & Punishment: Star Successor. It appears Nintendo "sandboxed" the Wii, perhaps due to hacking concerns. The Wii menu has the disc channel, Wii Shop Channel, and a program that lets users transfer data from a Wii to a Wii U.
Nintendo integrated the 3DSWare and DSiWare for Nintendo 3DS, but the Nintendo eShop doesn’t carry any content from the Wii Shop Channel. WiiWare and Virtual Console games are in the sandboxed Wii Channel. You still have those with Nintendo Points too.
I tried out Trauma Team, Trauma Center: Second Opinion, and Kirby’s Dream Collection on the Wii U. These three games played fine without any issues. You probably know this already, but Gamecube titles won’t work and unfortunately the Wii Channel is region locked.
