Well, yes, I posted this entry from my Wii using Opera browser and a usb keyboard.
For a new version of Wii, you have to buy the Internet Channel which is the Opera browser, costing 500 Wii points. It is fine in browsing www, posting blog, checking emails. It can't display Thai, though (of course, Thai input is impossible). The screen estate is quite important, because if you use Wii browser on a small screen TV, you can't read anything comfortably. The page have to be magnified using '+' button and contents need to be scrolled up and down, back and forth. Input system is quite awkward, needing to switch to the input screen everytime you need to in put text. Well it's not a good idea to use Wii internet channel for everyday use, replacing your PC (or iPhone :P ) browser. Just occasional browsing when you're stuck with your game on Wii is fine.