I've complied a list of great, lesser known movies, in case you get bored of all the well-known classics. All the movies under each period are in descending order of release date.

1964 - 1960: The Train, I Am Cuba, King and Country, The Gospel According to St. Matthew, The Night of the Iguana, The Killers, Passion, The Pawnbroker, The Soft Skin, The Lonely Wife, Blood and Black Lace, Pale Flower, Seven Days in May, Scorpio Rising, Nothing But a Man, Diary of a Chambermaid, Judex, The Servant, The Organizer, The Fire Within, Muriel or The Time of Return, Hands Over the City, Mahanagar, Le joli mai, Passenger, Legend of a Duel to the Death, Paranoiac, The Fiances, An Actor's Revenge, This Sporting Life, The House is Black, Le Doulos, Il Sorpasso, An Autumn Afternoon, The Fabulous Baron Munchausen, The Loneliness of the Long Distance Runner, Mamma Roma, An Occurrence at Owl Creek Bridge, The Pitfall, The Parallel Street, The Intruder, Salvatore Giuliano, Boccaccio ’70, The Miracle Worker, Divorce Italian Style, Paris Belongs to Us, Léon Morin Priest, A Raisin in the Sun, Il Posto, A Taste of Honey, The Exiles, Mother Joan of the Angels, The Human Condition III: A Soldier’s Prayer, Pigs and Battleships, The Naked Island, Late Autumn, Younger Brother, Zazie dans le métro, Rocco and His Brothers, The Good Time Girls, Le Trou, When a Woman Ascends the Stairs

1959 - 1955: Suddenly Last Summer, The Human Condition II: Road to Eternity, Floating Weeds, Fires on the Plain, The Great War, Black Orpheus, Nazarin, Good Morning, Letter Never Sent, The World of Apu, Les Cousins, The Human Condition I: No Greater Love, Window Water Baby Moving, Some Came Running, Murder by Contract, The Music Room, Ashes and Diamonds, Man of the West, Equinox Flower, The Fabulous World of Jules Verne, The Defiant Ones, Cairo Station, A Time to Love and a Time to Die, A Night to Remember, Giants and Toys, Big Deal on Madonna Street, Le beau Serge, The Ballad of Narayama, Bonjour Tristesse, The Tarnished Angels, Eroica, A Face in the Crowd, The Cranes Are Flying, Kisses, A Sun-Tribe Myth from the Bakumatsu Era, White Nights, Tokyo Twilight, Canal, Gervaise, There’s Always Tomorrow, Early Spring, The Burmese Harp, All the World’s Memory, The Unvanquished, Lola Montès, Richard III, Wichita, Summertime, The Big Combo, Floating Clouds, The Criminal Life of Archibaldo de la Cruz

1954 - 1945: French Cancan, Senso, The Caine Mutiny, Hobson’s Choice, Honour Among Thieves, Twenty-Four Eyes, White Mane, Thérèse Raquin, Él, The Naked Spur, Gate of Hell, Limelight, The Lusty Men, Forbidden Games, Le Plaisir, The Life of Oharu, Early Summer, The River, The Lavender Hill Mob, The Prowler, Boyhood, Miracle in Milan, The Flowers of St. Francis, The Sound of Fury, La Ronde, The Furies, Wagon Master, Night and the City, Thieves’ Highway, The Heiress, Obsession, The Silence of the Sea, The Set-Up, Blood of the Beasts, Portrait of Jennie, Germany Year Zero, Hamlet, Children of the Beehive, The Earth Trembles, Daisy Kenyon, Le Tempestaire, Nightmare Alley, Crossfire, Brute Force, Dreams That Money Can Buy, Paisan, Green for Danger, Canyon Passage, Sciuscià, Three Strangers, Ritual in Transfigured Time, Dead of Night, The Clock, Leave Her to Heaven, I Know Where I’m Going!, A Tree Grows in Brooklyn, They Were Expendable

1944 - 1935: The Private Life of a Cat, Murder My Sweet, Henry V, The Children Are Watching Us, A Canterbury Tale, At Land, Die Feuerzangenbowle, The Seventh Victim, Hangmen Also Die!, Day of Wrath, The Leopard Man, The More the Merrier, Portrait of Maria, The Palm Beach Story, Now Voyager, There Was a Father, Aniki Bóbó, The Murderer Lives at Number 21, The Major and the Minor, Shadow of the Thin Man, The Devil and Daniel Webster, Never Give a Sucker an Even Break, Ornamental Hairpin, The 47 Ronin, Ball of Fire, The Bank Dick, Remember the Night, The Letter, The Mortal Storm, Christmas in July, The Long Voyage Home, Night Train to Munich, Of Mice and Men, Another Thin Man, The Roaring Twenties, The Story of the Last Chrysanthemums, The Women, Daybreak, Dark Victory, Midnight, Port of Shadows, Olympia Part One: Festival of the Nations, Stage Door, The Prisoner of Zenda, Easy Living, You Only Live Once, Children in the Wind, Humanity and Paper Balloons, After the Thin Man, The Only Son, Fury, A Day in the Country, Mr. Thank You, Sazen Tange and the Pot Worth a Million Ryo

1934 - Beginning of time: A Story of Floating Weeds, Our Neighbor Miss Yae, The Scarlet Empress, The Black Cat, Les Misérables, Design for Living, Land without Bread, Japanese Girls at the Harbor, Gold Diggers of 1933, I Am a Fugitive from a Chain Gang, I Was Born But…, Love Me Tonight, Mädchen in Uniform, Tabu: A Story of the South Seas, Limite, Morocco, City Girl, People on Sunday , Woman in the Moon, A Cottage on Dartmoor, Diary of a Lost Girl, Lucky Star, Arsenal, L’argent, Show People, Storm Over Asia, The Wedding March, The Fall of the House of Usher, The Docks of New York, The Wind, Spies, October, The Crowd, The Last Command, The Student Prince in Old Heidelberg, The Unknown, Napoleon, 7th Heaven, A Page of Madness, The Adventures of Prince Achmed, Ménilmontant, The Big Parade, The Joyless Street, Strike, Faces of Children, Greed, He Who Gets Slapped, The Great White Silence, Kriemhild’s Revenge, The Thief of Bagdad, Siegfried, The Marriage Circle, The Wheel, Dr. Mabuse: The Gambler, The Golem: How He Came Into the World, Way Down East, Les Vampires, Cabiria, The Voyage Across the Impossible