Wii Online: Miiboard.com
Miiboard.com is one of the most full-featured Wii websites I've seen so far. It has an arcade packed with lots of flash games to play along with three pages of handy website links, a news section, chat and quite a bit more. The site design is very Wii-friendly with big links and a clean interface, so it's a great place to go when you venture onto the web from your Wii.
One of the most interesting features is Mii TV. With Mii TV users can post (embed, really) Wii-related videos from YouTube. Some are really interesting, but others are just plain… bad. Vote them up or down and rely on the "popular" link to prevent vomiting.
Use Miiboard to connect, chat and share with other Wii users right from your system. The site encourages interaction, so go there and start… interacting!