You didn't specify whether you want us to mention "Mafia" epics or simply other epics.

Action :

John Woo's Epics(Such as A Better Tomorrow 1 and 2, The Killer, A Bullet in the Head, and Hard Boiled )

Tsui Hark's Once Upon a Time in China Trilogy

Johnny To Films(Introduced Style Over Substance)

Crime :

Sergio Leone's Once Upon a Time in America

Martin Scorsese's Goodfellas and Casino

War Films :

In my opinion there are the three key films that are not just epics, but realistic masterpieces that brilliantly and realistically depict the war. These films are:

Michael Cimino's Deer Hunter

Francis Ford Coppola's Apocalypse Now

Oliver Stone's Platoon

Akira Kurosawa's Ran(Plus other films by this Japanese master, such as The Hidden Fortress, which influenced George Lucas to make the Star Wars Films)

P.S Yes of course there are a few others such as "A Bridge To Far" and "Saving Private Ryan", but to me these are the three key films. If you watch these there's simply no need to watch the rest.

Thriller :

Martin Scorsese's/Paul Schrader's Taxi Driver

Sidney Lumet's Dog Day Afternoon

Alfred Hitchcock's Masterpieces (Specifically films such as Vertigo, Psycho, and Birds)

Conspiracy :

Oliver Stone's JFK

Science Fiction :

George Lucas's Star Wars

Philip K. Dick's Productions such as Blade Runner

Horror :

William Friedkin's The Exorcist

Richard Donner's The Omen

Religious Epics :

Mel Gibson's Passion of Christ

Martin Scorsese's Last Temptation of Christ(Which coincidently was entitled "Passion" before)

Western

Sergio Leone's Classic's such as The Dollar Trilogy (The Good, the Bad and the Ugly, For Some Dollars More, and A Fistful of Dollars) and Once Upon a Time in the West.

Romance :

Arthur Hiller's Love Story

Comedies :

Some of the films these comedians made are indeed epics, but overall they influenced the whole subject of comedy in their countries(France and Italy)

Louis Ds Funès

Pierre Richard

Roberto Benigni