I want to play Mario Kart on Wii U, but I don't want to mess with the existing game data. Is there a way I can have my own separate profile?
Yep, just use a different Mii profile. Each Mii will have a different save file. Within your own Mii it is not possible to have multiple save games.
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1To clarify: not within the game itself, but in the upper-left of the WiiU main menu, you can tap to choose a different Mii-profile. – not-just-yeti Aug 25 '14 at 15:07