Here's what I can recommend:
Night of the Living Dead (1968) - The first film in George A. Romero's original "Dead" trilogy. It changed the landscape for not just zombie films but horror as we know it. Despite being cheaply made, the film still looks great in a lot of ways today. The film really played with the theme of disillusionment with typical institutions and the whole "the enemy is us" sort of idea.
Dawn of the Dead (1978) - The second film in George A. Romero's original "Dead" trilogy. The film is in color this time as our group of survivors find themselves trapped in a mall. Romero's commentary about materialism has only become more relevant and the larger budget means some better effects. Although time has not been kind to the "blueish tint" zombies, this is my favorite Romero film and all-time favorite horror film.
Day of the Dead (1985) - The third and last film in Romero's "original" trilogy. It takes a very bleak view as our group of survivors find themselves likely as some of the very few people still alive. At one point it's estimated the dead outrank the living 400,000 to 1. The main theme of science vs military never exactly came ahead as we have avoided nuclear apocalypse (for the moment) but it's still an excellent film.
Alien (1979) - Instead of trying to convince you, all you need is this trailer. Still an all-time favorite.
The Silence of the Lambs (1991) - Not your typical horror film by any means but it's the only horror film to ever win Best Picture. I wrote about it a bit last week here but Anthony Hopkins gives one of the best performances in a short amount of time.
Audition (1999) - Japanese horror film with one of the best build-ups of any film I've seen.
Halloween (1978) - The film that arguably set off the "slasher" genre of the 1980's but surprisingly very little blood in the film. One of John Carpenter's finest works as a mysterious figure known as Michael Myers goes on a murdering spree in his hometown of Haddonfield.
Also worth seeing from Carpenter in the "horror" genre include: The Thing (1982), They Live (1988)
Some of my favorite horror silent films in no particular order:
Nosferatu, The Cabinet of Dr. Caligari, The Phantom Carriage, The Phantom of the Opera (1925), and depending on how you look at it The Man Who Laughs (1928).
You've probably seen some of these but if I need to recommend a horror film to anyone, those would be it.