Will the Wii U render my old Wii games in HD?
No. In an
interview with Giant Bomb, Mark Franklin, head of PR for Nintendo, revealed that the Wii U would not "up-res" or upscale Wii games to an HD resolution.
Furthermore,
1up has provided a quote from Reggie Fils-Aime in which he says, in response to this question, "It will not do that. That's really driven by the hardware, and the original Wii games were built for a specific type of hardware. There's no mechanism to quote-unquote 'up-res' that unless we launch a brand-new game." However, the link provided for the source of this quote is a video where upscaling is not specifically mentioned, so this quote from Reggie is unconfirmed at the moment.
Finally, Ben Kuchera from Wired
reports that he was "flatly told" by Nintendo representatives that "the hardware will not be able to improve the resolution of Wii games."
It is important to note, that if you are using the old red, yellow and white composit cables on the Wii then yes, the games will look significantly better on the Wii U. This is because, the old RCA cables only offer 480i and not true 480p. If you bought red blue green component cables however then the games will look the same.