I think there's a broad sense in which any movie whose main goal is to horrify becomes a horror movie. Hence Psycho is a horror film even though nothing supernatural occurs. But eventually this parameter becomes pretty vague --- Diabolique or Repulsion maybe, but what about Cape Fear or Night of the Hunter. What I've noticed lately is how many police procedurals on TV like NCIS and such are drifting into horror territory, showing grotesque and horrible deaths in great detail in a way that was the province of giallo at one time.

Wow. That was a long one.