If you're looking for scares over violence and/or gore, you might want to start with classic horror. Monster movies. 30's - 50's. Or, skip right to the 60's and just do Psycho, The Haunting, The Innocents, and Night of the Living Dead. Many people say they think those films are scary and have little to no gore. As for post-60's, most people seem to hold The Changeling and The Omen in high regard. The Sentinel fits along those lines as well, but it's kinda goofy. Also, check out The Shining (1980), Don't Look Now, Alice Sweet Alice, The Wicker Man, The Lady in White, maybe Critters and The Gate (but they're also goofy), The Blob remake, Evil Dead 2: Dead by Dawn (also goofy), The Amityville Horror, Burnt Offerings, Ghost Story (1981, a little bit goofy), Christine, The Frighteners (goofiest movie you'll ever see in your life), The Sixth Sense, Stir of Echoes, The Others, The Mothman Prophecies.
That's the best place to start.