The Wii U most certainly uses the sensor bar. It just depends on how the Wii remote is being used.
In Wii Sports Club, only the accelerometers and gyroscope apparently are being utilized (except golf, which utilizes the gamepad's built-in sensor bar). This functionality similarly never required the ir array provided by the sensor bar on either the Wii or the Wii U.
But whenever the infrared sensor at the tip of the Wii remote is used (Most commonly as a "pointer" such as when navigating the Wii U or Wii dashboard), you need the sensor bar. The upcoming release of Duck Hunt on the Wii U Virtual Console will be a good example where it's going to be required.
And I suspect that Nintendoland also does in a few minigames for another example, although I've yet to really play it after briefly checking it out a year ago. I believe that Pikmin 3's optional Wii controller mode and Epic Mickey 2's multiplayer mode are two more examples where the Wii remote's infrared sensor is needed (And thus, you must provide it with a Wii sensor bar to look at).
Originally Posted by s1njin
The Pro controllers don't use the bar, and almost all the Wii U games (maybe all of them?) work w/ the Pro controllers.
There are many Wii U releases that lack Pro Controller support, although many of the best releases include support for it.
The already cited Epic Mickey 2 is one such example. Lego City Undercover also leaps to mind as one that I discovered doesn't include compatibility for this controller.
Even New Super Mario Bros. U, the system's premier launch title, didn't initially support it. Only when its expansion was released the next year was Pro Controller support patched in.