How much digital autonomy do your kids have?

A random question to those with children: how much autonomy do you (or do you plan to) give your kids over their digital identities and accounts - desktop files, email, social networks, et cetera? On the continuum between leaving them be entirely, and having full knowledge of all their accounts and passwords, where do you stand?

I recently blew up at a friend in email over learning that someone (not my friend) wanted to slip into their child's Facebook account so that they could use their friends-list to set up a surprise party. This struck a nerve with me, and I wrote an emotionally fueled reply. Today, in email apologizing for my outburst, I put into words, maybe for the first time, my conviction that one's digital spaces, both local and online, are very literally extensions of the mind. To me, access to your digital identity deserves the same level of sanctity as your personal one. Therefore, another person, no matter who they are or how kind and loving their intentions may be, has no more right to impinge on your digital spaces as they do to examine the thoughts in your head.

But: I didn't grow up in an internet-aware household, and I'm not involved with the raising of any of my friends' kids, so I have no experience in knowing how, or even if, this stance applies to children. I certainly accept that parents must have a great deal of direct control on the lives of their young children and teens, or they wouldn't be very effective parents. So, for my own education, I am genuinely curious how the smart and kid-enabled people I know treat this issue.