I think children should be allowed to watch horror movies, but judging movies on a movie by movie basis, and incorporating what you know about your kid. If you know your kid is still to immature to watch something, obviously they shouldn't be seeing it. But if you know your kid can handle the concepts in the movie, or at least can understand them after you explain them, I see no reason why they can't.
I was restricted from watching all horror films and anything with any violence in it when I was growing up. Not Freddy, not Batman, not the Karate Kid, not TMNT, not even the Bettlejuice cartoon (which I freakin' LOVE and am sure I would've loved as a kid) nothing. Zilch. When I was 18 I saw my first scary movie (Gremlins) and I had nightmares and had trouble sleeping for two weeks. At 18! This continued with subsequent movies (Zombie Lake, Poltergeist, Friday 13th...) All because I had never been desensitized to it. Go figure that now, at 27 one of my favorite shows is Dexter.... lol