LiveScience.com has a mathematical attempt to debunk vampires. It is pretty convincing. Basically, assuming vampires started several hundred years ago, and that a vampire bites someone every month which creates a new vampire, the spread of vampires would grow exponentially and there would be no living humans left to feed on by now.
That of course does not take into account the fact (as shown in movies and TV) that not all bite victims become vampires, many just die. It also neglects slayers, hunters, death dealers, and accidental exposure to sunlight.
Anyway, I don’t think kids are going to believe the vampire living in their closet doesn’t exist just because of a little math.