I have a 64GB flash drive in the back of my Wii U and it works perfectly. When I first bought the Wii U I had a small WD portable drive, but sure enough, without external power it wasn't always available and caused some problems with drive not being found, or updates getting put on the wrong storage. Only a few games seemed to be sticklers. Mario Kart was one, but figured I'd just try it with a thumb drive before wiring in more power and everything worked perfect.
So, if you're going the portable hard drive route, wire it to external power or use the Y adapter. Otherwise, a good size flash drive should work flawlessly without external power.