Wii browser?

The wi-fi part is built in to the Wii, to connect to a wireless internet connection. There is more on the browser itself on IGN.

From IGN:
May 23, 2006 - At the Electronics Entertainment Expo 2006, Nintendo president Satoru Iwata revealed that its forthcoming Wii console would be able to access the Web with the Opera browser. Iwata said that the Wii console could, "… power up virtual console games and applications like our Opera Web browser saved to flash ROM… in just a few seconds."

Yeah, I like Opera quite a bit, too, although I'm currently using Firefox because I like it's keyboard shortcuts and simple style. I really like Opera's "tab preview" feature, which basicly gives you a little screen shot of whatever tab you mouse over; very smart. It's pretty quick, too.
Opera is good, but for some reason on my computer Firefox is MUCH faster. But still, Opera on the Wii is gonna rock, just as Opera on the DS is gonna rock. I wonder if it'll be a free feature?
Wi-Fi is built into the system....its going to use a wireless router if you have one (if you dont im sure there will be some sort of cord or something) and the Wi-Fi connection is going to scan for the wireless router (btw..know that there is most likely going to be a limited distance) and when its detected ur online......
yes the WIFI and opera are supposed to be built in, the DS also comes with WIFI built in but you need to buy opera, there will be a usb wireless adaptor you can buy to connect the Wii and DS online if you don't already have one, if you don't want to go wireless there will also be a usb LAN adaptor for the Wii available. As for scanning for the wireless router yes there will be a limited range as with any WIFI, the scanning might not be available, you will probably have to set-up the wireless settings on your computer then very few on the Wii, they hopefully will include a disc for you computer to make all the settings so I don't have to go to all my friends houses and set-up their wireless connections.