When parents monitor their children's online activity they are doing nothing to teach them to guard their own privacy.
Cory Doctorow, my favourite author and blogger, gave a great talk at the TEDxObserver conference this past month. He believes that Facebook teaches our children to be less and less private by rewarding them for giving away information about themselves.
I am, by no means, a Facebook hater but I think Cory gives us some points to ponder about what kids are learning from the experience. I do LOVE his idea about teaching them to not accept being spied on by anyone (parents, schools, local businesses, etc.) and to value privacy as a diminishing commodity.