I like some horror, although I'm still new to the genre. I used to be pretty squeamish and it wasn't until I snagged Netflix this year that I considered watching some of the ones I'd missed.
The Fly: Cronenberg's remake of the horror classic is easily my favorite horror film of all time, and probably one of my favorite movies overall. I knew most of the story before I watched the film, and the premise so disturbed me that I had trouble sleeping for a few days. At its core, the film itself isn't that scary--it's what you'd expect from well-made body horror, which is to say it's a damn fine thrill ride. More importantly, it's a character story that really resonates. Jeff Goldblum and Geena Davis are at their best here.
The movie will not scare you, but it counts as a horror film simply because of the setting, theme, and how the story unfolds. It's more like a gothic horror (think Edgar Allen Poe) in a modern setting, which gives it a timeless charm. While it doesn't succeed at being scary, the strength of the screenwriting and characterization are the most important elements in any film, so I still count it as my favorite horror. The original's good too, but very different. Both are worth checking out.
Kairo: One of the first horror films I sat down to watch. It's a quiet and subtle Japanese ghost story, but it has such an oppressive atmosphere, and such mesmerizing sound design, that I'd count it as the scariest movie I've ever watched. Basically, the story concerns people who are disappearing and turning into ghosts, and the main theme of the film is loneliness. The loneliness is very artfully emphasized--awkward lines of dialog show how distant people are from each other, and it only gets worse as the film goes on.
To my recollection, there's no gore, nudity, or language, yet this movie somehow still scored an R rating in the states. I'm guessing it's strictly because of how frightening it is.
The Exorcist: This movie's a classic for a reason. Like The Fly, I wouldn't say it's scary, but once again its strength lies in the characters and their interactions. The viewer is led to feel real sympathy for the family who's going through all of this, as well as the priest performing the exorcism.
A good bit better than The Omen, which was influenced by The Exorcist and starred...well...the antichrist. That movie was unintentionally hilarious all the way through.
The Phantom of the Opera (Silent Version): The Phantom is a classic movie monster, and the setting and music paint a brilliantly horrific picture. Classic gothic horror at its best. As a fan of the original story (and gothic horror in general), I couldn't be more pleased!
Jacob's Ladder: Does this count? If not, it's still a damn good movie, and it's disturbing enough that it at least deserves mention on this list. Helped inspire the Silent Hill series, which I'm too scared to play (I sampled 2 hours of Silent Hill 2 before ridding myself of the game). A damn good movie in its own right, with just enough subtlety to keep things mysterious and enough characterization to call it a drama as well as a psychological thriller.
Alien: Of course! I hate slasher films, and this is kind of like one, but it's told so elaborately that I'll forgive that misstep. You might know about the chestburster scene, but there are probably a couple of twists you're not aware of before you watch the movie--I know it caught me by surprise! The imagery is really strong here--you won't see special effects this convincing and memorable nowadays, in the age of CGI.
You'll hear that the sequel, Aliens, is better from a lot of people. Don't believe them. The first movie was a real horror, with real intensity; the second movie is, by comparison, a kind of mindless action movie with few thrills to be had. As is the case with the Terminator franchise, the first movie is the best because resources are used well here. Nothing's overdone. One overpowered alien is much scarier than hundreds of aliens.
There are probably others, but I'll stop there for now.