My mum was constaantly on my case about chatting online to unknown people. She used to tape things off the TV about the dangers of internet predators all the time. I never really convinced her enough that I was being extra careful, not giving out lots of details and things. When I did get close to one person and exchanged phone numbers with them, she obviously fretted again. But she appreciated that when I did finally meet up with him (3 years later) that I told her where I was going, and was taking 2 friends with me. I imagine there's a good chance she spied on me, god knows she still tries to today (though I'm much more computer wise these days, much better at covering my tracks... (sorry all you parents, but the day will come...))

My advice would be to educate them and make them wary, but don't overcrowd them. And if you're going to spy, make sure you only approach your kids if it's something really serious.