Nintendo released a demo of their browser for the Wii. It seems to work pretty well for checking the weather, email, google. I tried a few of the kids sites like NickJr, but it only played some of the flash content. The videos didn't work since they were windows media. Since I can now check Weather.com using the browser, I doubt I would use their Forcast Channel.
If you have a Wii, try WiiCade which has some good games optimized for the Wii. There are also some wii flash games at Albino Black Sheep Wii Games; but I havent tried them so I cant comment on the quality of the games at Albino. WiiCade had certainly done a good job making a Wii optimized page, and providing good games.