Maggie Smith’s 1969 Oscar-winning performance as the title character, a teacher at an all-girls school in Edinburgh in the 1930s who intones that “all my girls are Brodie girls, and they are the crème de la crème,” is one for the ages. With her eccentricities and love of the arts, she is hard to resist, until she starts to confuse the glories of the Italian Renaissance with the rise of Italian fascism.

Fred Schepisi’s 1984 film is a one-of-a-kind triumph-of-the-spirit movie. Archaeologists stationed in the Arctic uncover a man frozen in a block of ice for millennia. The team doctor (Lindsay Crouse) is able to bring him back to life. Timothy Hutton plays the archaeologist who crosses the impossible boundary into this survivor’s long-vanished culture and becomes his friend, and John Lone is the iceman. The movie’s debate over the relative values of science and anthropology is fatuous, but it’s a stirring, surprising picture, and Lone’s ingenious, mostly physical performance is one of the great forgotten pieces of film acting of the late 20th century.

This 1981 MGM release should have brought musicals back, but it bombed at the box office and wound up being the last great musical for two decades (until Chicago). Steve Martin plays a down-on-his-luck song plugger who dreams of opening his own music store; Jessica Harper is his dour, long-suffering wife and Bernadette Peters is the schoolteacher he tumbles for. The period is the Depression, which is also a symbol for the unhappy lives in which this trio—as well as some vivid supporting characters—is bogged. In the amazing musical numbers, the actors open their mouths and the voices of popular singers of the 1930s waft out of them, giving expression to emotions the characters are too blocked up to release on their own.

An exuberant CinemaScope musical that badly needed the DVD format to recover some of its lost glory. Stanley Donen directed this 1954 adaptation of a Stephen Vincent Benét story about a family of brothers who go shopping for wives in the Old West. Michael Kidd choreographed the glorious, athletic dances, which include a barn-raising number and “Lonesome Polecat,” a plaintive mock-ballet in the snow. The mostly wonderful songs that Howard Keel and Jane Powell sing are by Johnny Mercer and Gene de Paul.

Arguably Alfred Hitchcock’s wittiest thriller, the film features Robert Walker as an elegant sociopath who meets tennis celebrity Farley Granger on a train and proposes “criss-cross murders”: Walker will kill Granger’s blackmailing estranged wife (and leave him free to marry a senator’s daughter) if Granger will eliminate Walker’s tyrannical papa. The movie careens into a delirious triple climax—a tennis match Granger must win in record time, Walker’s efforts to recover a lost cigarette lighter, and a struggle on a merry-go-round gone out of control.

Korean director Kim Ki-duk’s film plays out entirely on a small floating monastery in the middle of an isolated lake, where an aging monk takes a series of aspiring monks under his wing, teaching them lessons about kindness, humility and patience, while the students confront their longing for romance and desire for revenge. Beautifully photographed, every frame of this quiet film speaks to the gaining of wisdom and the inevitable passage of time.

A satire about what might happen if all the Mexicans disappeared from California. Though not as cutting as it might be, it’s a cautionary tale about indifference and about how racial intolerance can lead to economic chaos.

In the 15 years since his death, director John Cassavetes has gone from low-budget filmmaker to independent cinema god, thanks to a body of work that wrestles with adult problems. This 1974 effort is one of his best, starring his wife and muse, Gena Rowlands, as an emotionally disturbed wife and mother who, despite her best efforts, can’t seem to be what everyone close to her wants or needs. The film is a series of wrenching scenes that showcase her pain, especially in confrontations with her working-class husband (Peter Falk), who longs for the funny woman he once knew.

“You don’t make up for your sins in church. You do it in the streets. You do it at home. The rest is bullshit, and you know it.” So begins this trailblazing 1973 film that announced the arrival of director Martin Scorsese. The tale revolves around a pair of childhood Italian friends who are going their separate ways. Johnny-Boy (Robert DeNiro) is a screw-up who attracts trouble, while Charlie (Harvey Keitel) is looking to become a “made man.” His journey is complicated, however, by a load of Catholic guilt that causes him to stick his hand into the flames just so he can sense what the fires of hell will feel like.