The "Giallo," one of Italian horror's most important subgenres, got started in the early-60's with such films as The Girl Who Knew Too Much and Blood and Black Lace -- both directed by Mario Bava, who along with Dario Argento, made the genre's initial great films. They were then joined by the likes of Lucio Fulci and Umberto Lenzi, whose popular giallos have been discussed in this thread. I probably like the ones by Argento the best (e.g. Deep Red), especially because of his intimate collaboration with the great Ennio Morricone.