Supernatural Drama

Make sure you check out Angel Heart, as Holden listed, as well. That film pulls no punches. A true neo-noir, but with the required supernatural elements you asked for...

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Fallen, Ghost Story, Strange Days, Interview With A Vampire and Poltergeist are the ones mentioned here that I liked the best.

Another film I really liked that hasn't been mentioned yet was Frequency (2000) it's one of the rare time travel sort of movies that's really good.

Butterfly Effect was another time travel sort of film that worked but it was totally different. I was so jealous that those actors got to play all those lovely flavors of the same characters. Do not bother with Butterfly Effect two, it was pathetic.

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Bleacheddecay

Holden and Rufnek each said it very well. I was scared twice by movies, myself. 'the Others' and Hitchcock's ' Psycho'. I thought 'the Uninvited' and ' the Haunting' (the one with Julie Harris ) were among the best movies I ever saw but they didn't scare me.
'Seance' is, also on my best picture list but I didn't remember it as being scary. I liked 'Jenny' which I'd recommend for you as not being too scary.

The Others' was a good one for me. I liked the twist. I was waiting for it the whole time but didn't know exactly what form it would take.

It reminded me a bit of Sixth Sense that way. I had a great big ? mark over my head while watching both of them. LOL!

Identity was a little too slasher for me but I like it nonetheless because of the huh factor and twist.

Devil's Advocate...This is a good movie and definitely has sense...

Suspiria, eXistenZ, The Fury...sort of fall into the psyche-horror category but aren't scary from what I recall.

Ironically Angel Heart stands as the only film that ever made me throw up and I'm really not sure why. I own it now and haven't exactly been able to recreate the effect.