People who know me personally know that I am a bit of a cryptography buff. One of the first things I ever did with logic programs in Excel was to build a very stunted and useless One-Time Pad calculator. I routinely change passwords according to a set of predetermined rules. Hell, I even pre-encrypt backups and key files, many of which never leave the hard-drive on my computer. If my position statement on PIPA/SOPA and related legislation wasn't enough of a clue, I value privacy, and in a digital age, that means maintaining strict control of systems and files, never mind the much more complex issue of social networking.
Locking down data tables is so easy that a child could do it... and they often do. I usually had my account on the computer pass-locked and put passwords and sometimes even full encryption on files I wanted to keep private, going back to my first year in high school. If I wasn't such a homebody, my parents would have been hard-pressed to keep any sort of track of my activities... and now that's even more true than ever before.
The question, then, is how much privacy to allow children on the computer, and what you do about it when they circumvent your stated rules. When I used to tool around on CAF, I used to get any of a number of responses. Some parents said that they used software web blocking tools (such as those often used by schools and offices) to block websites with varying levels of strictness, up to and including one father who allowed only white-listed sites... those he specifically approved. Other parents installed keystroke recording software -- commonly called "Keyloggers" -- or even hardware, to record every input their child made to the computer. Keystroke logging, especially on the hardware side, really is the 'nuclear option' when it comes to keeping track of what your kids are doing. You'll have every URL typed, every line of text, every manually-typed password.
In the end, though, however you go about it, there's always flaws to any net-guardianship scheme. For one thing, children are often more computer-literate than parents, and if you were a real computer nut like I was, you took pride in getting around any obstacle placed between you and total computational freedom. Then, there's the human factor: nobody likes to think their parents don't trust them. Hard as it may seem to believe, kids don't like to feel like their parents are always watching them. That problem gets even worse when the child owns the computer in question. (ProTip: Your teen daughter might own her laptop, but you own the power and internet coming into the house.)
Me? Well, I don't have kids. If I did, though, I'd be honest. It's not them I don't trust. It's the internet. And if you want to use a computer connected to my network, you best believe I'm going to be sure your computer is safe... both in terms of net security, but also in terms of your life.