In the latest Nintendo Direct (via NeoGAF) that aired today in Japan, Satoru Iwata shed light on the USB storage options for the Wii U. Since at most you'll be getting just 32 GB of storage built in, you're likely going to want to shop around for an external hard drive.
Right out of the gate, the Wii U's initial firmware will allow you to use a USB storage option that is up to 2 TB in size. You will be able to store data and run games off of the device, which should certainly come as a major relief. The device will need to be formatted for the Wii U, which means you won't be able to use it to store data from other devices. As of right now, the console will only support one hard drive at a time, but the plan is to add support for two in the future.
On a slightly more disappointing note, backwards compatibility leaves a bit to be desired. All original Wii games, Virtual Console and Wii Ware titles can't be played on the GamePad screen. There are however, plans to bring Wii U-specific Virtual Console support that will include GamePad functionality sometime in the future.
Iwata addressed the issue by saying, "We understand that there are people who were looking forward to playing Wii games, Virtual Console games, and so forth on the GamePad, but unfortunately we cannot accommodate those users' expectations."
THAT'S IT, I'm canceling my pre-order right now! Ha, just kidding, I didn't pre-order one anyway.