The plot of Carol Reed's The Third Man follows Holly Martins (Cotten), an American author who goes to post-war Vienna at the behest of his friend Harry Lime (Welles). When he arrives, he finds out that Harry has died in a bizarre car accident filled with coincidence, suspects foul play, and tries to get to the bottom of it. The police are reluctant to help him and are in fact glad he's dead. They believe he was a racketeer who profited on the misery and suffering of children in need of penicillin. Harry's lover Anna Schmidt (Valli) disregards their opinions; even if it is true, it doesn't change who he was to her and the love between them. The plot brings up unique viewpoints on betrayal vs. friendship, love to one person vs. duty to all mankind--all very ripe for discussion about your own beliefs.
In fact, I find the characters surprisingly deep. When Martins tells the police that Harry was the best friend he ever had, the police responds that it sounds like something from a cheap novelette. Martins writes cheap novelettes. Perhaps he's written so many he becomes the cheap novelette himself. We later find out they hadn't talked in ten years; is that really the best friend he ever had?

IMDb link: http://www.imdb.com/title/tt0041959/