Yes, horror movies can scare me. Horror is my favorite movie genre, even though almost all horror movies are pretty bad.
First one that ever really scared the crap out of me was A Nightmare on Elm Street in the movies when I was a kid.
I wonder why that movie worked so well in its ability to scare. I think it is because it was about dreams, and we have all had dreams that are truly frightening.
Even as I get older I find that I can still be scared, but it's not by special effects or blood or monsters, it's by the unknown.
A couple of movies that have worked very well in scaring the s*** out of me was Insidious, Devil and Frailty.
None of those movies was big budget or had any special effects that are memorable, but what they had was very clever plots and the element of fear came from the unknown factor in each movie.
Insidious was about a boy who astral travels when he sleeps and runs into a nasty spirit along the way. Devil is about three people trapped in an elevator, and one is not what they seem. There are no special effects in this movie, all of the fear generates from the dialogue and events and the possibility that what of there really is a devil and he really does stuff like this...
Frailty is also a personal favorite. This movie starred and was directed by Bill Paxton, a truly great actor, it had virtually no special effects, and it generated fear by showing killers, a man and his two boys, who were doing what they were doing because of the father being a religious zealot, but then at the end it becomes unclear if he was a zealot or if he was actually doing exactly what he said he was doing because it's real.
I think it boils down to two things. The first is that someone has to conceive of and write a smart plot and second has to keep in mind that it's not what we see that scares us, it's what we do not see, and it's not what we know that scares us, it's what we do not know.