Any action rpg. A touch screen is a great way to manage real-time inventory.

Anything multiplayer. Card games. Pokemon battling.

And shooter. The HUD is soo cluttered on them these days. Put ammo, mini-map, health bar, XP meter (COD), and real time score info on the controller, leave the TV to just display the game.

Basically any RPG/Strategy/RTS game with a complex UI system or requires you to multitask like WoW, Starcraft, Pikmin, Dragon Age, etc. This is actually one of the few exciting potentials I see in this controller, as I've been waiting for some good console RTS games ever since the Wii launch. Dawn of Discovery was about the closest I got to one.

As I see it, here is a number of games that benefit from the WiiU video controller:
* Card games or other games with hidden information, you want to hide from other players, assuming that the WiiU allows more than one of these. Play selection screens in American football would be ideal on the Wii U. Poker night with a WiiU would be interesting.
* RTS and other strategy games. Being able to drawn and point on the screen makes RTS finally have a shot of being doable on a console in a good way.
* The stuff that Nintendo showed. Seeing the golf ball on the ground, is really cool. The sniper option is also cool.
* Games with level editing. Using the touch screen is very helpful for editing, more so than a Wii-like pointer device.
* Boardgames. Having the WiiU controller as your main way to interact is very helpful. Touch to the screen rather than play on the big screen is more natural.
* Driving games. The screen on the controller can act as the dashboard, and also include a rearview mirror.
* FPS and other action games. Declutter the HUD on the screen. Also have the inventory immediately available.
* In a FPS, one player could play commander with the touch screen and order other players around to take over command points on the map.
* Wariorware, as someone mentioned.

And this just scratches the surface of what can be done.

Edit: Another one is games where there is needs for the controller layout to change based on context in the game.

Okami - I mean come on
Fire Emblem - select and move units around with touch screen, unit stats and battles on the TV
The Witcher 2 - touch screen quick menue and potion crafting/drinking
Civilisation

EDIT: OH fuck The World Ends With You!!!!

Trauma Center games obviously, Mario Paint, Battalion Wars, Driving games could work really well without the need to buy a steering wheel, same for Flight games...