Every time we have seen the Wii U console itself it's always been sat horizontally. That's because the system is designed so it can't stand vertically. In an interview on Kotaku, Shigeru Miyamoto explained why. He explained that like with Microsoft's Kinect, that the physical hardware is not the face of the system.

"Similarly with Wii U, when we [considered the question] ‘What is the face of Wii U going to be?', for us the face of Wii U really isn't the console box itself. It's the controller; it's the Wii U GamePad. So just like a set dop box is non-descript and tucked away, our feeling was that the Wii U hardware was something that could be tucked away and out of sight.