The majority of "slasher" or serial killer films bore me. I'm just not one to react with a genuine chill to blatant physical horror/repulsion. I like a little more finesse, myself. I like something that gets in there and niggles at you with intimations and adumbrations, rather than smacking you in the face with a cold mackerel. Not all such films are of that type, no. But a huge majority of them on this theme are, sadly. No reason you can't have a truly disturbing and haunting piece about a serial killer -- it's been done: Robert Mitchum in Night of the Hunter is a good example, for instance; or (again, Mitchum) that throroughly nasty type, Max Cady, in Cape Fear (1962; I've not seen the remake, but Mitchum's was quite nasty enough....).
However... among those that have always haunted me: The Haunting (1963) by Robert Wise. So many superb moments in there because you're never really sure about things... and you don't really see what it is that's haunting Hill House... only hear it, or see its effects; so your imagination can really go to town.
Several of the films Val Lewton produced would be on my list; all understated, but that allows them to get in there quietly and disturb all the more. The Seventh Victim (1943), for instance. Can even seem slow and plodding, a little silly at times... but it builds toward a very ... effective ... ending. That last screen moment still sends a chill up and down my spine.....
Or I Walked with a Zombie (also 1943); I don't know whether Darby Jones' Carrefour or Christine Gordon's Jessica Holland are the more unsettling (or more pitiful) zombies(?) here. But the creepiness here is the pervasiveness of a culture's superstitions, and the question of whether they have a basis in reality or simply in distorted thinking... but how they affect lives, and make monsters of even the most innocent....
There are others I'd put on the list. The original Night of the Living Dead certainly did it for me the first time I saw it -- in a packed-house, primed like a keg of gunpowder waiting for the match. Very effective that way, it is; genuinely terrifying.
I quite like the original Japanese version of The Ring and, as Nesa said, Dark Water. Also Ju-On (The Grudge). All of those were very effectively scary films, much better than the "in-your-face" sort of thing, and can still get the hair up on the back of my neck after repeated viewings. The American version of The Ring left me cold, unimpressed. Too much flash and glitter, not enough subtlety and substance. Alejandro Amenábar's The Others is another one, in some ways. Also Guillermo Del Toro's The Devil's Backbone. And, in some ways, Stuart Gordon's Dagon, though that one had to grow on me. Didn't care at all for it the first time out, but now it's become a personal favorite... and it gets creepier each viewing, as the genuine eerieness factor is understated, and -- appropriately, for a film on that theme -- surfaces when you least expect it....