There are two classics, already mentioned: Call of Cthulhu and Chill.
For Chill, I prefer the second edition. For Call of Cthulhu, the mechanics have on the whole been pretty stable. Any version based on the BRP system should be fine, so long as you don't have power gamers and watch out for some of the unbalanced supplemental material often intended for NPC's but which when coopted by PC's gets stupid.
Call of Cthulhu is about cosmological horror. It's about finding out the world itself is antithetical to human life, that human reason is futile, that human resources are inevitably insufficient, that human religions and philosophy are false, that truth is unknowable, that logic is useless, that human science and progress merely will lead to humanities inevitable undoing. The horror is very much philosophical, and the forces you are facing are vast and marked by great indifference to mankind and suffering. The horror here is discovering that you are little more than some insect to be devoured or parasitized by something vastly beyond your understanding and completely unconcerned with you.
Chill is a smaller more personal sort of horror. Here the universe you know is being invaded by things that are actively and perversely evil. They not only are aware of your suffering, they enjoy it and feed on it. Instead of fighting vast indifferent cosmic entities, you are fighting back things that go bump in the night and the darkly familiar monsters of human myth - werewolves, vampires, hags, and worse things.
Both can be truly frightening if done well.
The hot new kid on the block is one I haven't played and which I'm not sure how you'd run until I've seen it demonstrated well, and that's Dread. Dread as I understand it is designed mainly for one offs, typically emulating something that might be an episode of the Outer Limits or a horror movie, with a cast moving toward some inexorable doom. It seems to have a lot of fans, but it is a very different experience from a traditional PnP RPG.