Can Old Wii Controllers Play New Super Mario Bros. U? No

No. New Super Mario Bros. U is a Wii U game. It requires Wii U controllers:

• Wii U GamePad (primary, touchscreen)
• Wii U Pro Controller
• Wii Remote / Wii Remote Plus + Nunchuk (supported in NSMBU)
• Classic Controller / Classic Controller Pro

What Doesn't Work

• Original Wii console – cannot play Wii U discs (different format, encryption).
• GameCube controller – no native support in Wii U mode (adapter only works in Wii Mode / homebrew).

If You Have a Wii U

Your existing Wii Remotes (Plus) + Nunchuks work perfectly. No new hardware needed unless you want the Pro Controller or GamePad replacement.