Do regular Wiimotes work on the Wii-U?

Yes, regular Wiimotes are supported by the Wii-U.

This page on Nintendo's website says:

Controllers

The Wii U console is capable of supporting two Wii U GamePad controllers, up to four Wii Remote (or Wii Remote Plus) controllers or Wii U Pro Controllers, and Wii accessories such as the Nunchuk, Classic Controller and Wii Balance Board.