Night of the Hunter really stands out in my mind as a classic despite the fact I have only seen it once. Directed by Charles Laughton (who you may remember as Moreau from The Island of Lost Souls), this is based on the true story of a guy who traveled around killing widows and children.
Robert Mitchum is great as Powell, the "preacher" who drifts from town to town killing sinful women. When he ends up in a cell with Robert Graves, who has just robbed a bank and hidden the money with his children, he hatches a scheme to grab the hidden money after Graves is executed. Mitchum seduces and marries the now-widowed wife of Graves (played by pre-fat Shelly Winters) and terrorizes the kids to try and find the loot. When the new wife gets suspicious, Mitchum gets to murderin'. The titular night takes place as the orphaned children flee from Mitchum to an older woman's house. I won't spoil anymore if you haven't seen this classic yet.
The whole thing feels like a thriller wrapped around a subtle jab at organized religion. By making Mitchum's character a preacher, Laughton demonstrates the power of the pulpit to make common people blind to gross indecencies. The townsfolk love Mitchum's character but just as quickly turn on him later in the movie. These fickle hypocrisies leave one with lots of tough thoughts about just which wolves the Shepherd is protecting his flock from.