I have one word for the possibility of a real, actual tooth fairy: CREEPY. Not only does she sneak into children's rooms at night, but she takes their baby teeth away from them. NO. That is just so wrong. However, even thought it would be less creepy for a tooth fairy in a different form to carry out the duties, it still would be wrong. Just wrong.
All right, imagine that in Europe there is a small species of animal (lizard, insect, rat, frog etcetera) that takes the teeth from corpses for some reason. These would either be an undiscovered species or a type of behavior in a known species, a behavior we haven't seen before. Human teeth are as good as any other teeth, so human teeth are sometimes taken by these animals. This happened to some people centuries ago. Unable to explain this phenomena, the few people who had this happen to them began to circulate the myth of a tooth fairy. Nowadays, even in America, where these species do not exist (or do they), the tooth fairy myth is still popular.