No, you can connect through cables. Or so I heard... I haven't got one of these Nintendo Wiis yet so I can't say for sure.
You can, IF you buy one of
these(which use up 1 USB Port).
^^They don't start shipping until January 2007!
Do you need to plug in a fast ethernet cable in the Wii?
Uhm.
Nope.
I'm pretty sure the only way the Wii can access the internet... is through a wifi connection.
Y'know, like the DS?
So the Nintendo USB Wifi stick would work?
Yes, the above page confirms it:
"you can use the Nintendo Wi-Fi USB Connector to connect your Wii console to your broadband internet connection through your existing PC."