10. The Ex-Mrs Bradford (1936)
Whilst not strictly a detective movie (William Powell here plays Dr. Bradford), there's a fair amount of sleuthing to be had, as dark shenanigans at the racetrack result in a baffling murder. Dr Bradford's murder obsessed ex-wife, Paula (Jean Arthur) shows up at exactly the wrong time and throws the hapless, peace loving doctor into the middle of a smart whodunnit. With terrific support from the ever dependable Eric Blore as Stokes, the butler, and a solution you just won't see coming, it's an underrated classic.
Bradford: "In exactly 28 minutes I have to start opening a gentleman's stomach. Maybe I can do as much for you some day"