I used to watch a lot of mafia films and there are a number that stand out as true classics. I have compiled a list of my favorites here (ordered by production date) so that fellow mafia film fans can check them out.

The Public Enemy (1931)	An early James Cagney film
Little Caesar (1931)	An early film starring Edward G. Robinson as a crook named Rico that claws his way up the ranks of the mafia.
Scarface (1932)	The oft-missed original version of the popular 1983 version. This one stars Paul Muni and is much more sober in its depiction of the tragic main character.
Angels With Dirty Faces (1938)	A really good film with James Cagney playing a hood that tries to be a role model for younger kids after getting out of prison.
The Roaring Twenties (1939)	James Cagney stars as a bootlegger in the 1920s.
White Heat (1949)	Made it, Ma! Top of the world!
On The Waterfront (1954)	Marlon Brando plays a washed up boxer that reluctantly takes on the mafia, who control the longshoremen.
The Godfather I (1972)	The classic adaptation of Mario Puzo's model
The Godfather II (1974)	The equally stunning sequel
Scarface (1983)	Al Pacino's modern Cuban drug dealer take on the original Scarface
Once Upon a Time in America (1984)	Sergio Leone's epic bootlegging saga, following a group of young Jewish friends through their lives.
The Untouchables (1987)	A somewhat cheesy and very inaccurate film about the government's take down of Al Capone.
Goodfellas (1990)	Scorsese's classic film adaptation of Henry Hill's life story
The Godfather III (1990)	The final installment, which didn't do nearly as well as the first two
Miller's Crossing (1990)	A story about two rival gangs and one man who profits from both of them.
State of Grace (1990)	A story about two gangsters who bring an old friend back in the fold, not knowing that he is now a cop bent on bringing down their organization.
Billy Bathgate (1991)	A film about a young man that becomes a friend to Dutch Schultz, the ruthless bootlegger.
A Bronx Tale (1993)	Robert de Niro's film about a young boy growing up under the influence of his saintly father and mob boss idol.
Carlito's Way (1993)	An excellent film starring Al Pacino about a reformed drug dealer trying to retire and start a new life.
Casino (1995)	Scorsese's adaptation of the Pileggi book of the same name, focusing on organized crime in early Las Vegas.
Donnie Brasco (1997)	The mostly true story of an FBI agent going undercover in the mafia, starring Johnny Depp and Al Pacino.
Road to Perdition (2002)	Tom Hanks and Paul Newman star in a rather serious film about a young boy and his gangster father.
The Departed (2006)	A modern crime saga involving two moles, one in the Boston police department and one in the Boston Irish mafia.