Listing here sound-era titles prior to the great one itself, Psycho ('60), that come to mind featuring out-and-out murdering psychos. Sex-crazed killers are included, but I'm excluding cuckolded lovers (with an exception or two), supernaturally possessed one-or-two-off killers, murderers-for-money, thieves who kill, criminal masterminds and other villains (i.e., "film noir psychos"), mad scientists and revenge killers, however maddened. Just plain ordinary psychos who kill because they have a screw loose --randomly or out of perversion/horniness.
Please supplement as you see fit:
M ('31), Murder by the Clock ('31), Central Park ('32), Doctor X ('32), Unholy Tales ('32, German, based on Poe), Murders in the Zoo ('33) (borderline, but Lionel Atwill kills repeatedly because guys are eyeing his wife... so it's not really a "revenge" killing), Night of Terror ('33), Charlie Chan at the Opera ('36), Night Must Fall ('37), Black Limelight ('38), They Drive by Night ('39), Case of the Frightened Lady ('39), East of Picadilly ('40), Calling Dr Gillespie ('42), Spiral Staircase ('45), Boston Blackie's Rendezvous ('45), Lured ('47), Without Warning ('52), Violated ('54), Alias John Preston ('56), The Night Runner ('57), Devil Strikes at Night (German, '57), It Happened in Broad Daylight (German, '58).
What did I leave out? Did I include anything that doesn't fit? I know there are a lot of borderline and judgment calls involved here, but would welcome feedback.