Wiiminder

Wiiminder is a tabbed-browser-emulator for the Wii Opera.

Wiidiscover

Wiidiscover is a Web Community to find people to play online games with a Nintendo Wii console system.

Wiilu

Wiilu is a Diggit clone oriented to Wii news and with a Wii-easy-browsing interface. In spanish.

Wii Video 9

Wii Video 9 is a free video conversion application developed by Red Kawa. It allows you to convert your computer video files (like avi, divx, mpeg, etc.) into the specific video formats that are playable on the Wii.
Wii Video 9 can also be combined with Videora, another software application, and together they can let you automatically download and convert video for your Wii using BitTorrent and RSS technology.

Wii Media Center X

Wii Media Center X is a free multimedia server developed by Red Kawa.
It allows you to stream certain types of pictures, music, videos and files from your computer (where the server running) to your Nintendo Wii.
It runs on most major operating systems including Windows, Mac OS X and Linux.
I haven't test it yet.

SofaTube

SofaTube is a YouTube interface to be used from the Wii. A bit confusing in my opinion, as all videos listed appear as sticky notes, and they can easily transform into a mess of floating squares. Just tested for 5 minutes.

Finetune

Finetune is a internet radio station optimized for Wii browsing.