Here is a list of websites you can watch videos and movies using your Wii Browser. Wii Browser uses Flash so almost any flash based video playing website will be compatible with the Wii Browser.
You can go on almost any website, because Wii has Flash player, and you can do almost anything with that. Also, here are some links:
http://www.hulu.com – great for free (legal, owned by NBC) tv shows
http://www.imeem.com – internet radio, awesome
http://www.instructables.com – how to, DIY etc.