I beleive it will use the same wi-fi usb connector as the DS? It will use it for downloading retro games also. Im also hoping that most games will have an online functionality. Not just the odd few as with DS but every game with a multiplayer should go online in my opinion.
Also, in case you didnt know this, the wii can stay online all the time. This is called wiiconnect24. This way, friends (almost certainly using friend codes) will be able to send you gifts (animal crossing) , messages, etc while you sleep/ are busy.
Problem is, i cant stay online ALL the time as i have AOL silver, and, due to them being a pain i have to use a differnat connection for playing on my DS. Oh well. presumably anything sent to me will arrive the next time i connect.
Hope that was what you were looking for. And of course, none of this is guaranteed; nintendo, being nintendo could have anything up their sleeves...