Hook up a hard drive
The Wii U, like its predecessor, is lacking a hard drive. What paltry internal storage it does have is capped at 32GB, and that's only with the console version that costs $50 more. But thankfully, it's never been easier to simply hook up an external hard drive to the console and store everything on that.
It's a simple process, and if you can honestly find enough downloadable items on the Wii U to fill up a terabyte of storage, then good for you. For most people, though, it'll be more than enough.