I don't think of it as Internet Safety so much anymore rather I like to call it Internet Awareness or Internet Literacy. If you have an understanding on what's going on on the Internet, you are much less likely to become a victim (and I mean adults as much as kids). One of the things you need to know about the Internet is that there is really no such thing as privacy. This Venn Diagram* is wonderful at explaining this concept... you should show it to students.
Of course, why use one visual when two will do... seriously, the Internet is not a private place, even if all your settings are set to private. A good rule of thumb is assume people can see what you are doing. Sure, this means you have to watch what you post, where you surf and such, but better to start this habit now.
Related to privacy is the fact that we are all growing more connected to each other as a result of our interactions on social networks. The video below is a bit old (Friendster, really?) but it visually shows these connections.
*note to self, do a post on Venn Diagrams sometime in the future.