I suggest you read bp9801's article, Nintendo Announces Wii Successor - Wii U before this one. Also, I'm calling the console the Wu and while I don't know if I am the first to do so, I am certain I won't be the last.
This new console brings from Nintendo its first HD offering, supporting full 1080p HD and multichannel audio. So what exactly is it that we'll be seeing in 1080 vertical lines and 5.1 surround sound? Watching the videos found at Nintendo's E3 website you can see some of the games coming to the console (Wii U Demonstration)
Not on the Nintendo site, though still shown at E3, there is a video where you can see either the Wii titles or Wu versions of New Super Mario Bros, Go, Wii Sports, Wii Fit, a shooter that uses the Wu controller for a rifle scope, a game having you throw Ninja stars by swiping them off of the Wu controller touchscreen, a Legend of Zelda game,
most likely a Wu designed build of Skyward Sword. Edit: In a video interview by Gametrailers with Nintendo of America President, Reggie Fils-Aime, this is referred to as just what a Legend of Zelda game could look like on the Wu (around the 0:25 mark). Comparisons of this video to video of Skyward Sword show a clear difference in art style. Skyward Sword is more a return to the Wind Waker cell-shaded styling, while this Wu demo appears to be of the Twilight Princess styling.
Naturally we'd expect there to be Nintendo games on their upcoming console. At the Nintendo E3 site you can view a Third Party Developer video:
It would appear the Wu will not initially suffer from a lack of hardcore titles, as many state the Wii does. Engadget also lists Batman: Arkham City and an Assassin's Creed game as coming to the console, though they were not shown in the video.
UPDATE: The video of the third party titles did not contain video of the games rendered on the Wu. More here: The Wii U Games NOT All From Wii U.