When my kids grow a little, I am definitely going to respect their privacy especially when it comes to their use of the Internet. Of course, in order for me to respect their privacy they are going to need to grow so that they are older than they are right now.
Of course, when your kids are still small but are already capable of surfing the Web, you should check all websites that they visit on the Internet regularly. Nothing should escape your attention and you should make sure that you are aware of any potential dangers lurking all over the Internet and threatening your children.