“Wake in Fright” would be a good example. It could all be true - nothing supernatural, no CGI… “The Housemaid” (1960) is another example, but I didn’t like it. “Rosemary’s Baby” would NOT be a good example (I won’t spoil why)… “Eyes Without a Face” and “The Face of Another” (even better) are very good, and have been classified under this category.
“Fist in Pocket” (Bellochio) might be one of my favorites, if not my favorite. Italy, 1965ish.
The original “M” might fall under this category, but I think many would consider it a thriller/mystery, but its great.
I was a veteran of all the horror genres through the 80’s when I first saw it and Carol’s crazy eyes when she stops, then continues slashing at the landlord still gives me the willies!
I can’t believe I forgot the great “Peeping Tom”… Are there ANY movies similar around that same time? The closest thing I can come up with is “The Collector”, which isn’t that close, but just as good.
I’ll throw in The Haunting (1963), based on Shirley Jackson’s The Haunting of Hill House. (And not to be confused with the 1999 ‘remake’) Haven’t read the book or seen this version in many years, but as I recall, there were no actual spookies shown, just implied, and a case could be made for it all being in Eleanor’s head. One of my favorites nonetheless (goes to hunt the DVD/Blu-ray…)
I’m not sure where other people draw the line between horror and thriller. For my money Robert Mitchum played the villain in a couple of the best non-supernatural horror films: Cape Fear (1962) and Night of the Hunter (1955). The latter is loosely based on the career of a real serial killer.