The latest update allows players to transfer data between Wii Us.
Previously, you could do a one-time transfer from a Wii to a Wii U, but there was no way to transfer data from a Wii U to a new Wii U. With update version 5.1.0, a "System Transfer" option is now available. You can learn more about that feature by heading here. Another new update moves the eShop away from exclusively using the GamePad, and lets players use a Wii Remote, Wii U Pro Controller, or a Classic Controller to navigate the shop. Otherwise, the only other update note is "Further improvements to overall system stability and other minor adjustments have been made to enhance the user experience."
For details on the previous update, which added the helpful Quick Start Menu, head here.
Thanks to Clint for the news tip!
[Source: Support.Nintendo]

Our Take
The ability to use other controllers is one of those things that seems like it should have already been available. Using the GamePad is realistically probably the best and easiest way to navigate the shop, but options are always nice.