The best thing I've heard to tell your children is to find a mother if you're lost. It makes sense because a mother would not let your child be alone and they're readily identifiable to children. They're also more prevalent than police (or store employees, if you've ever noticed).

Aside from that, all of our kids (except the 1-year-old) have memorized our phone number and know how to spell their names and ours.

We have taught our daughter to try and remain calm if she is lost. To not cry as this could draw extra unwanted attention. She knows that it is better to wait than to wander off searching and that if she is approached by any people, she should not go off with them.
We have explained quite thoroughly the different types of uniformed people that could be helpful, and she recognises the difference between security guards and policemen and other persons of authority.

We recently thought about giving her a card with our mobile numbers on them, for possible emergencies and I am happy to say that she knows our home address by heart.

Edit: Although we have never experienced any incidents, I think its really important that your parents, inlaws and other family members are also made aware of your "plan of action" should such an incident take place while your child is in their care.

We used to put a card in their pockets containing our cell phone numbers. We told them to always stay where they are (if you're in the woods, "hug a tree") and we'd find them.

From a totally paranoid point of view, if you're at a mall, don't tell your kids just to find a policeman or security guard, since anyone can buy a security guard uniform and walk around the mall. We were told to tell our kids to go into a store and talk to someone behind the counter and they will call mall security.

This question was featured in Issue #3 of the Moms4mom Newsletter, and the newsletter contains some more info.

My four year old I never let go of so I don't really have to worry but I have told her if she can't find me then to just sit down and wait for me to come back.

My eight year old I bought her a cell phone that she keeps with her all the time. She can call friends on it yet so I know there are always minutes on it. I have told her to sit where she lost me and call or go to someone that works there and ask them to call me.

Good ideas to think about...my daughter is only 11 months, but I will have to think about it soon enough!! You should find out what your child's school or day care teaches about strangers....I always had a unit on Strangers/Safety in my Kindergarten class.

I once heard advice for when you're children run away at the beach repeatedly: just write the number of your cell-phone on their foreheads.

But I personally would only put that in practice as a worst case scenario.