I wish this was something we covered a lot more in my media effects class. Children, as mawk and others say, do not have to be exposed to something to know that it's bad. A kid doesn't sit down at the computer giving out their address everyday on a YahooChatroom or what have you everyday, but it does happen, and normally these kids think that such an action is okay to do, because some caregivers don't say 'now when you're online, don't X Y or Z'. If YOU, as the parent, know how to use a computer (which a fair share of us here do) then I think a lot of these horrible scenarios of kids being exposed to all sorts of things can be easily prevented. It's the same thing with television and such, which was what I focused most of my studies on.
In regards to kids on the internet, a 9 year old requested to be my friend on Facebook. Wonderful. <_<