Parent are off doing their day job, kids are home and online in their rooms. When my kids were young we had one computer for them to use, and it was in a fairly public area of the house. We had their passwords, and we check browsing history. If anything was deleted or passwords changed they were off the computer until they could convince us to trust them again.

I worked from home and converted the dining room (which was next to my office) into the game room, so the TV, computer, and Internet connection was there. Kids forget you're just a door away from what they're saying, so I kept up with a lot. Same thing with carpooling - the things I learned! Once wireless came about, I changed the password regularly. But I think being involved with your kids is also another important aspect of keeping them safe online.