I'm not sure I'm a judge of what people should see in such absolute terms so perhaps you'll forgive me for listing a few that are personally significant without suggesting any obligation to view them.
Il Gattopardo (
http://en.wikipedia.org/wiki/The_Leopard_(film)) (AKA The Leopard) by Luchino Visconti, based on the novel by Giuseppe Tomasi di Lampedusa, starring Burt Lancaster, Claudia Cardinale, Alain Delon.
"If we want things to stay as they are, things will have to change."
"We were the Leopards, the Lions, those who'll take our place will be little jackals, hyenas; and the whole lot of us, Leopards, jackals, and sheep, we'll all go on thinking ourselves the salt of the earth."
Medea (
http://en.wikipedia.org/wiki/Medea_(film)) by Pier Paolo Pasolini, with Maria Callas.
Le Petit Soldat (
http://en.wikipedia.org/wiki/Le_Petit_Soldat) by Jean-Luc Goddard with Muchel Subor and Anna Karina.
Scum (
http://en.wikipedia.org/wiki/Scum_(film)) by Alan Clarke (dir) and Roy Minton (Wr). With Ray Winston.
The Killing of Sister George (
http://en.wikipedia.org/wiki/The_Killin ... ter_George) by Robert Aldritch, with Berryl Reid, Susannah York and Coral Browne.
Unforgiven (
http://en.wikipedia.org/wiki/Unforgiven) by Clint Eastwoon. With Eastwood, Gene Hackman, Morgan Freeman and Richard Harris.
Les amants criminels (
http://www.imdb.com/title/tt0205735/) (AKA Criminal Lovers) By François Ozon with Natacha Régnier and Jérémie Renier.
Tokyo Drifter (
http://en.wikipedia.org/wiki/Tokyo_Drifter) by Seijun Suzuki. West Side Story (
http://en.wikipedia.org/wiki/West_Side_Story_(film)) by Jerome Robbins and Robert Wise. Love in the Time of Cholera (
http://en.wikipedia.org/wiki/Love_in_th ... era_(film)) by Mike Newell, from the novel of Gabriel García Márquez. The Warriors (
http://en.wikipedia.org/wiki/The_Warriors_(film)) by Walter Hill. Ararat (
http://en.wikipedia.org/wiki/Ararat_(film)) by Atom Egoyan. The Mission (
http://en.wikipedia.org/wiki/The_Mission_(film)) by Roland Joffé. Laila Ma Raison (
http://www.imdb.com/title/tt0116842/) by Taieb Louhichi. Les Enfants Terribles (
http://en.wikipedia.org/wiki/Les_Enfant ... les_(film)) by Jean-Pierre Melville and Jean Cocteau.
There, I exceed the quota by one.

No particular order except that Il Gattopardo is first and foremost.