I'll start with Henry Mancini's "Main Title" from Orson Welles's Touch of Evil (1958):
Here's Duke Ellington's wonderfully swaggering"Upper and Outest" from Otto Preminger's Anatomy of a Murder (1959):
I've always responded like a Pavlov dog to the sound of a theremin on a movie soundtrack.There's something about the instrument's quivering, imprecise, other-worldy tone which causes instant cognitive dissonance. We know that something abnormal and possibly dangerous is happening, either inside the head of the character we're watching, or, in the case of science fiction films, to our planet. The Soviet inventor Léon Theremin patented his creation in 1928, and it was first used in a film score by Shostakovich for 1931's Odna. But it was eighteen years before it graced a Hollywood movie: Miklós Rózsa used it for Hitchcock's Spellbound (1949) to convey Gregory Peck's psychosis: