So far I've only seen Zombie (Flesh Eaters), but wouldn't mind checking out some more. Critically, his films weren't well received, but thought it was worth asking horror fans themselves.

Don't Torture a Duckling (1972) -- A very good giallo with excellent social commentary.
Zombi 2 (1979) -- Splatter Horror Classic! One of the best zombie films ever made.
The Psychic (1977) -- A splendid supernatural thriller with a great ending.
The Beyond (1981) -- Strange but fantastic demonic horror with awesome imagery.
Contraband (1980) -- Fulci's best attempt at an action thriller. Very violent.
Murder Time (1966) -- Excellent spaghetti western made at the height of the western craze.

Middle of the Road:
The New York Ripper (1982) -- Brutal and nasty slasher. Not for everyone, read about it before watching.
The House by the Cemetery (1981) -- Decent, if someone convoluted and confusion, gory ghost story.
City of the Living Dead (1980) -- Not half-bad horror movie with some truly impressive gore effects.
Perversion Story (1969) -- A psychological erotic thriller and early giallo.
Four of the Apocalypse (1975) -- Well-done psychedelic revenge western. Unlike any others.
A Lizard In a Woman's Skin (1971) -- Odd giallo film with a lot of psycho-sexual themes.

And, His Less Celebrated Works:
Zombi 3 (1988) -- Cheesy but fun zombie horror, however don't expect anything "good."
Murder Rock (1984) -- Pure 80's camp slasher. If you like 80's music, check this out.
Manhattan Baby (1981) -- Not as terrible as some reviews suggest, but still not a classic.
The Black Cat (1982) -- Late giallo/early slasher with supernatural themes. Not great.
A Cat in the Brain (1990) -- Pretty poor, when Fulci had really hit the skids.
Conquest (1983) -- Hokey fantasy swords and sandals film. Not as great as you'd expect.

Zombie 2 The only scenes I even remember are the eye splinter and shark fight (which I have a shirt of, but nevertheless).