After hearing the Wii U details and eyeing some trade-ins, you might be tempted to head down to your local games retailer and give them your Wii. We'd advise you to wait, at least if you want to keep all of your old data and purchased Virtual Console games.
A Nintendo representative confirmed to Gimmie Gimmie Games that a content transfer from the Wii to Wii U will require you to have both systems connected to the Internet at once. The rep compared the process to transferring between the DS/3DS family of systems.
That transfer will include all of your Miis, WiiWare, and Virtual Console games. You probably don't want to have to repurchase those games, so best to keep your old neglected Wii around for a while longer.