Other than downloading VC games? Wii is on the complete opposite side of the house from the wireless router and barely gets signal so I havn't bothered setting it up.
I find personally that my devices work best when the system software\firmware is left intact in it's factory configuration. Thus my wii is not on the internet.
First online game supposed to be in 07. I THINK (I'm probally wrong) the 1st online game is SSMB or the new Metroid. One of those. But like I said, I THINK (my memory sucks at 3am).