A recent article in Smithsonian.com classifies a scene from the 1979, movie, "The Champ", starring Ricky Schroder and Jon Voight as the saddest in films. According to the article, the clip is used widely in psychology labs to evoke sadness in subjects.

The scene features a nine-year-old Schroder crying over a dying Jon-Voight, his father in the movie. The scene fetched Ricky Schroeder a Golden Globe. The movie, by director Franco Zeffirelli, a remake, about a washed-up boxing champion making a comeback, did not do too well at the box-office.

The experiment to find movie clips to evoke emotions of sadness, greed, laughter etc in laboratory settings was started by Robert Levenson, a psychology professor at the University of California, Berkeley, and his graduate student, James Gross in 1988. Levenson is a professor at Stanford University now.

They collected 250 film clips, whittled it down to 78 edited clips of varying durations and showed them to 500 viewers to determine their emotional responses to the films. Finally in 1995, they published a list of 16 short film clips able to elicit a single emotion of anger, fear, disgust laughter or sadness. Their research has been cited in more than 300 scientific articles.

Used in innumerable experiments to determine sadness, the clip has helped scientists to gauge behavior of people when they are sad. They found that people are likely to spend more money when they are sad, older people are more sensitive to grief and sadness does not lead to an increase in binge eating, according to Dutch scientists.

Films are something you go to willingly to experience sadness, joy, fantasy etc and as Gross says, “films have this really unusual status. People willingly pay money to see tearjerkers — and walk out of the theater with no apparent ill effect. As a result, 'there’s an ethical exemption’ to making someone emotional with a film.”

There may be many who can come up with their own list of films that were real tearjerkers. Our emotional moments in stories are driven by our connections to the character and personal experiences. But there is something universally sad about a young child crying over the death of a parent.

Levenson and Gross also found the fake orgasm scene from "When Harry Met Sally" that evoked maximum amusement.
Anger: My Bodyguard and Cry Freedom
Disgust: Pink Flamingos and an amputation scene
Fear: The Shining and Silence of the Lambs