I'm wayyy under 35, but anyways:
1) Psycho
2) The Shining
3) Halloween
4) Alien
5) The Birds
6) Scream
7) Deep Red
8) Videodrome
9) Rosemary's Baby
10) A Nightmare on Elm Street
Top horror lists infuriate me because the genre line is so often blurred. Jaws, The Silence of the Lambs, Dressed to Kill, and Dead Ringers might all make the list, but I don't know if they really count as horror.
I kind of agree with you here, most people now only consider violent gore filled films such as Saw and Scream to be horrors and disregard other titles and say they aren't as good, calling them psychological thrillers.
I'm 17 and films like Psycho, The Shining, The Birds, Silence of the Lambs and others I all find brilliant. Just because they are more based on suspense and psychological shocks doesn't mean they aren't as brilliant. I found Psycho genuinely scary and Silence of the Lambs certainly has a lot of horror aspects in it especially the scenes with Hannibal.
Other than those I've mentioned I haven't seen that many horrors, not a massive fan of newer ones and much prefer older ones such as The Exorcist. Carrie I really want to see as well as well as Alien and Aliens.
Scream I quite like, the first one at least but newer versions of Friday 13th and Nightmare on Elm Street are terrible in my opinion.
So yeh horror films I've seen and would recommend:
Psycho
The Shining
The Silence of the Lambs
The Birds
The Exorcist
Scream (first one is best, second decent, other two meh)
Jaws
Saw (the first one, rest are terrible)
Blair Witch Project (need to see it properly/fully but was very good I thought)