Do you think kids should watch scary movies?

I grew up LOVING scary movies. My dad said I would sneak in at 2-3 years old and watch them until thy noticed and took my out. I mean I loved paranormal, Gorey, everything. It didn't make me violent or give me nightmares. My daughter is 19 months and loves them. I try to watch them when she's sleeping but sometimes she wakes up and wants to cuddle and she watches it. We watched death note tonight and she sat and watched the whole thing and loved it. It really wasn't scary though.

What are your views? And why?