Raging Bull (1980)

Directed by Martin Scorsese

The story of boxer Jake LaMotta from his fighting years to his later years as a nightclub owner.  It might just be Scorsese's best picture.  Great story, great storytelling, looks brilliant.  Uses the black and white to maximum effect.  Scorsese often tells stories about violent characters that don't fit into society that well.  This is one of the best examples.

Mean Streets (1973)

Directed by Martin Scorsese

This is an early example of Scorsese's now well tread genre: the crime picture.  First major role for Harvey Keitel, and a very early one for De Niro as well.  The budding talent is jumping off the screen here.  Has more of a loose indie-film feel to it than Scorsese's later work.  Not as caustically violent as his later gangster pictures.