First off, some decent answers….I’d honestly stay away from the Saw series….the first one was kind of imaginative, but really it degenerated as the sequels came about (they always do) into just a bloody mess, and even the first one is really, really gory. I have no problem with that, but if you’re going to do gore, you’re best to go with Rob Zombie films like House of 1,000 Corpses, The Devil’s Rejects or his Halloween remake, they are the height of brutality, particularly Devil’s Rejects…one of my all time favorite horror movies and one of the few that I actually found to be “scary”, though having a serial killer theme, may not be for you.
The thing about horror was that in the early 70s when you had classics like Texas Chainsaw Massacre and the Exorcist, the fear was more about suspense, really building up the tension to scare you big time when the really scary scenes happened, as opposed to much of the modern horror which is all about trying to keep you on the edge of your seat…it’s the movie equivalent of jumping out and saying boo in my opinion.
That’s one reason I didn’t like some of the films mentioned….The Ring and The Grudge, I can see why they were popular, but I’d definitely go with the original Japanese versions of these films…I kind of felt like the story/concept was good, but it was ruined by them trying too hard to scare you and not really letting the fear wash over you and take over.
And I have to say, no offense intended to @jaketheripper, but everything he posted, with the exception of 1408 (which I say you’re better off reading Stephen King’s short story to be honest), was in my opinion perfect examples of that modern kind of horror filmmaking which really forgets about suspense and just tries to creep you out in some way. Not bad if that’s what you’re into, but I suspect that’s not what you’re going to be into. Some examples of what I’m talking about…take the Number 23 for example. Dude starts seeing the number 23 everywhere, and the film just degenerates into, “omigod, the number 23,” repeat ad nauseum. And the Haunting in Connecticut, supposedly based on a “true” story, but basically the real story is really boring and most of what was reported by this family that was haunted was inconsistent from one family member to the next, but this made it look like every 10 minutes something scary was jumping out at you…I felt it lacked imagination…very much been there, done that for me.
Poltergeist, at least the first one is definitely a good choice, and someone mentioned Audition, these are more what I think you’re going for. The Orphan is perhaps one of the best of this type of horror film in quite some time, very good, mostly original story with a killer twist ending, and the fear is just more palpable…it reminded me of a movie from the early 90s called The Good Son, which I think is also a good choice. Some modern movies that got the suspense/horror thing down right in my opinion are The Sixth Sense, The Others and What Lies Beneath, all great suspenseful horror movies with twist endings you really don’t see coming. Someone mentioned Blair Witch, and that one was REALLY effective on a big screen in the dark, I’m not sure you can get the proper effect on that one if you see it on DVD, but it’s worth a shot.
A lot of people mentioned the Shining, and yes, I’d go with that one, but make sure you get the theatrical version featuring Jack Nicholson, not the made for TV version with I think Tim Daly….here’s a rare example of where I disagree with the author on this one…though I think we’d both say “read the book, it’s better”, King was unhappy with the theatrical version, whereas most film fans and critics, even those who loved the book, think this is an all time great horror movie. Now, with Stephen King though, rarely do you find a movie as good as the book, however I have to say the recent adaptation of The Mist, was perhaps the best adaptation of a King book I’ve ever seen, I HIGHLY recommend that because of the way the suspense builds into outright terror.
Another one I enjoyed quite a bit was called the Gravedancers….it was a really good supernatural story which also had some pretty nice effects towards the end. Anyway, that ought to be enough to get you started.