N.,
I think it's important to remember first that about 100 children are abducted by strangers every year in the US. Sometimes we assume it's one million per year and we teach our children with that mindset. (800,000 children do go missing every year, but 200,000 are abducted by family members, 60,000 by people they know and the rest are run aways.) We tell our children that people they don't know are out to get them and they should be afraid. The chances of them being abducted by a stranger are so incredibly slim, but the chances of them becoming paranoid, insecure or unduly stressed out are very high.
I think the other big mistake we make is that we send mixed and confusing messages to children. "Don't talk to strangers" but we expect them to be polite and talk to the new Pediatric nurse or day care provider they have never met. "Don't ever take candy from strangers" but you can have a sample cookie from the baker or a sucker from the bank teller. That's very confusing. I had a friend who taught her almost 3 year old daughter who was still in diapers never to show her private parts to anyone. Then she sent her to my house for the whole day and her daughter wouldn't let me change her diaper. She had to sit in a dirty diaper until I could reach her mom and she was available to get her. We really need to think these things through as parents.
I tell my children that if they are offered food, they ask mom before taking it. If they want to pet a dog that belongs to someone at the park, they ask me to accompany them. They are welcome to talk to people the they don't know, but I need to be right there with them. This has worked very well with even our smallest children. The bottom line is they need to be watched closely.
To be honest, even if we do scare the heck out of our children and tell them to be afraid of everyone, to fight back if taken, etc. most children are going to freeze in that kind of a situation. We have this fantasy that our children will listen to our counsel and act with amazing courage and strength in a situation where most adults would panic.
I saw a Dr. Phil episode where children were tested to see if they would follow counsel about stranger danger. All the kids in the test group knew the right answers in a classroom setting, but when one of the show producers showed up at the park and asked them to get in the car to see his puppies, they all ran right into the empty car. Until children are older, they just need to be supervised because they lack the judgement to protect themselves.
With my school aged children, we talk more about never leaving with anyone regardless of the story they give you. We also talk about internet safety and have rules about what you can put on the internet, what websites you can go to, etc. We talk about appropriate touch, how it's okay if the doctor asks you to pull down your pants, but not other people. But we don't obsess over that kind of thing, talk about it frequently or be dramatic or agitated when we discuss it. In my daughter's Kindergarten class, the counselor told the kids not to play near windows because predators may be watching them. It's been 3 years and my daughter still has a hard time going to sleep in her room because she fears being abducted in the night.
Good luck,
S.