In my teens - when I tended to read horror novels rather than watch horror films - I was very struck by a Stephen King short story (might have been a Richard Bachmann one) about a man left on a desert island who literally started to eat himself in order to survive. The question of how far a person is prepared to go in order to survive is one that I find very interesting (have to discuss that with my therapist!) and this film is the definitive exploration of the theme. The sequels are dreck, the 'influenced' films - like Hostel - are even worse.
4. A Nightmare on Elm Street (1984)
One of the earliest horror films I saw, at a very impressionable age (I'd guess 15 or so). The central conceit is excellent - Don't fall asleep! - and there are plenty of genuinely scary moments, but the reason why it abides in my mind is the ending, when Nancy turns her back on Freddie, thereby denuding him of power. Profoundly true...
3. An American Werewolf in London
This was the first horror film I can recall watching - at about age 12 (yes, much too young) - and it gave me all sorts of nightmares for ages. Yet, as with that scab that you can't help picking at, I have returned to this film periodically over time in order to slowly overcome that dread. It contains one of the scariest sequences I've ever seen (the repeated dream) and it's also very funny.
2. Land of the Dead
This was the first Romero I ever watched, and sparked an interest in the zombie genre which is ongoing (I loved The Walking Dead - I'll have to read the comic). Again, it is the conceptual weight which makes the movie - the vision of rich people in a gated community, holding back the eager hordes whilst they seek to preserve an illusory existence. Prophetic stuff.
1. The Exorcist
Well what else would it be? Despite some of the OTT schlock, a profoundly orthodox work which treats the material seriously. What the devil seeks is for us to see people as ugly, and that is the direction to which all his temptations tend. The faith wins a victory when it sees as Christ sees - and that is what despatches the devil to his den.
Of course, these are subject to change over time, and an old one - like The Shining - might squeeze in. Let the Right One in will probably get in there before long (haven't rewatched it yet).