My brain is pretty scrambled at the moment, so I'll just name off a random assortment of movies. Don't assume that I have good taste!
Pumpkinhead (1988) is a good "starter" horror movie. It's not too frightening or gory, and the "southern Gothic" set design and lighting help to set the film apart from its contemporaries. Not too impressive in terms of acting (aside from Lance Henriksen as the lead) or storytelling, but it's a decent slice of backwoods horror. Plus, Pumpkinhead is an iconic monster design.
Visiting Hours (1982) is a surprisingly well-acted (and plotted) Canadian slasher flick. Michael Ironside steals the show as the film's misogynistic antagonist, but the rest of the cast holds their own admirably. In my opinion, this is a cut above the usual slasher fare.
Prince of Darkness (1987): Science, religion, and horror collide in this oft-overlooked John Carpenter film. It's no Halloween or The Thing (then again, what is?), but it's an interesting footnote in Carpenter's portfolio.
Halloween III: Season of the Witch (1982): Go into this blind (and drop all of your pre-conceived notions regarding the Halloween franchise). This is a weird movie. The eighties were weird!
Bad Dreams (1988): A young woman, critically injured in a cult's mass suicide, awakens from a decade-long coma only to be haunted by the malevolent spirit of said cult's leader. Some consider this to be a rip-off of A Nightmare on Elm Street III: Dream Warriors, and honestly, I'm inclined to agree—although the set-up is different, the setting, characters, and plot are quite similar to that of Dream Warriors, albeit with a few twists. On the other hand, the film has some snappy dialogue and a wonderfully creepy performance from (a sadly under-used) Richard Lynch as the creepy cult leader antagonist. The movie doesn't quite reach its full potential, but it's an interesting curio.
The Manitou (1978): This is another movie that you need to go into blind. It takes a while to get going, but when it does, it doesn't let the fuck up. Best viewed with an audience!
Also try:
Hellraiser
Suspiria (1977)
Phenomena (1985)
The Serpent and the Rainbow
Black Christmas (1974)
Poltergeist (1982)
Dead & Buried
The Brood
Just Before Dawn
Mimic
Near Dark
Cronos
Phantasm
The Fog (1980)
The Hitcher
In the Mouth of Madness
The House on Sorority Row
Ginger Snaps
Not quite horror, but contain horrific imagery (or atmosphere):
Nightbreed
Lord of Illusions
Alice Sweet Alice
Campy fun:
Shocker
Chopping Mall
Sleepwalkers
Night of the Creeps
Night of the Comet
Sleepaway Camp
Dolls
Q: The Winged Serpent
The Guardian
Mirror Mirror
Terror Train
Prom Night
Prom Night II: Hello Mary Lou
Rawhead Rex
An American Werewolf in London
Ghosthouse
House
House III: The Horror Show