The Wii LAN Adapter will begin shipping in early January 2007.
The Wii LAN Adapter allows you to hook your Wii console to your wired home network in order to access your broadband internet connection.
So, if you have a wired router, you can use the LAN Adapter to physically plug the Wii to the network. Your PC will not have to be on unless you have an internal cable/dsl gateway installed in your PCI slots (rather than an external stand alone model).
I don't know if a normal USB to Ethernet adapter would work. I would say no. Currently, no USB device can be utilized by the Wii. This suggests that Nintendo may limit what USB devices can be used.
