Mii channel was my favorite.
Although, the internet channel served a legitimate purpose back then. Laptops and modern TV's weren't as common. Wii had some limited Flash support, but it was enough to run youtube and other video sites. You could also play certain flash games, there was a site that listed a few that were playable on the Wii.
I remember also being able to browse on Orkut at the time, which was the Facebook counterpart at Brazil. (except it had forums!)
Using the online platform Meebo you could even talk people over MSN, although it was really impractical to use there.