The Thing (the original one) is good too. That blood scene. My God. And Alien.
Just to be clear, when you say the original The Thing, do you mean John Carpenters The Thing or the 1951 film that was based on The Thing From Another World?
Oh and speaking of the Shining, there is a level in the game Vampire: The Masquerade - Bloodlines that is a massive love letter to that film, and whilst not as bone chilling, is an effectively terrifying mission, in fact in terms of pacing and it's understanding of horror, that entire section puts most dedicated horror games to shame.
Although not strictly horror, I do love a good slasher flick, by which I don't mean anything involving paranormal immortal killers, I mean the kind where the killer actually stalks and lays in wait, the kind of films that build up tension to a knife point before delivering the scene, which is usually just a grab and your imagination left to do the worst part.
Conversely the Exorcist 3 is a masterpiece, I highly recommend it.
Also speaking of knife point tension, Hellraiser, just the first one.
And finally I have to, Human Centipede 2; is a genuinely disturbing, well shot, unnerving almost Lynch-esque dive into the obsessive mind of a mentally disturbed psychopath... just don't watch the second half, because the second half just kills it with lunacy.
Also again, whilst more of a thriller than an actual horror movie, the original Saw movie is absolutely fantastic, highly recommended, doesn't make a big feature of the ironic traps, instead it's an amazing film driven entirely by the two protagonists trying to figure out why they were picked for the game and who it could be that put them there.