There are parental controls on the Wii that can limit the access of internet websites to "friendly" websites, but if you're kids are smart that'll hardly stop them from finding any OTHER websites. On the other hand, its harder to go online on the Wii unless you have a wireless USB keyboard, so kids my age prefer actual computers. Its just easier since you don't have to pick up the mouse every time you want to click something and put it back down when you want to type like you would if you had to use the Wii-mote. Also, if you have a secured Wi-Fi connection at home, as long as you have the WEP key or whatever key your network has, you'll be able to use the Wii on your secure network, just like you would on a laptop.
The Wi-Fi connectivity of the Wii is just the same as an iPod touch, a laptop, or a PSP.
In most cases, its difficult to get onto an unsecured network. On the wii, you're usually too far from a neighbor's wi-fi to even be able to connect and have a steady connection. It'll usually disconnect within a matter of seconds unless your close enough and have minimal interference.
If you have anymore questions about the Wii, I'd be happy to answer. I'm a Wii-freak.
