Most sites are Wii Friendly, However, here are some programs usually run on internet sites that the Wii can't use (from personal experiences, some programs may work on certain sites) :
-Java
-Flashplayer (Sometimes! most of the time though it works)
-Macromedia
-ActiveX (confusing though, sometimes it works, sometime it doesn't, guess it depends on your Wii's mood
)
Some Genre-Specific sites that never work for me:
- Video Game sites (ones that only run on Flashplayer, Java, etc.)
- Music Sites (music doesn't load)
Hopefully this helps where and where you don't navigate on the Internet Channel!