Warning: this list is hopelessly weighted toward the 1980s. The '80s were not a particularly good decade for film, yet it is the decade in which I came to love the movies, not to mention that '80s films are almost always available on video. To my mind, there's no use telling you to run out and see anything you can not locate because there is plenty that you can find that you should see. And on that note, I confess that this list is also hopelessly weighted toward American (that is, U.S.) product, because these are the films that video stores chain and local in the U.S. always carry. Films are listed alphabetically.
The Empire Strikes Back (1980) / Star Trek II: the Wrath of Kahn (1982) / Flash Gordon (1980) / Aliens (1986)
Four big, widescreen comic books. Flash Gordon is too silly, Star Trek II is too serious, Empire is too George Lucas, and Aliens is a shade too long, but all four are great fun and have soundtracks worth owning. Of course, the sound effects, special effects, and production design are all impressive (even now). These are films (mostly) for boys who dream of flying to the stars and shooting bad guys with laser pistols.
Forbidden Games (Jeux interdits) (1952)
A war film that does not show war, a trait it shares with Jean Renoir's The Grand Illusion. Directed and co-written by Rene Clement, it's perhaps not as dignified as Renoir's film, but more emotionally involving and a stringent denouncement of war.
The General (1927)
Buster Keaton's Civil War film is plotted with such precision it reminds one of an expensive watch. The Great Stone Face is funny in films like Steamboat Bill Jr., but this film fully demonstrates the creativity of the greatest silent film comedian.
It's a Wonderful Life (1946)
This Frank Capra film is the most cynically life-affirming film ever made. Folks who claim to hate this film secretly cry when they watch it. James Stewart is perfectly cast as the Everyman who worries he has missed out on life only to find out that his life has indeed been wonderful.
The Ninth Configuration (1980)
This may be the definitive movie-you-have-not-seen-but-should. William Peter Blatty (author of The Exorcist) writes and directs this ridiculous film about Stacey Keach in charge of an asylum, conveniently housed in an old Castle. The endlessly quotable dialogue almost distracts you from the unfolding story.
Raising Arizona (1987)
Joel and Ethan Coen's hyper screwball comedy features Nicolas Cage as a would-be reforming robber and Holly Hunter as his police officer wife. Cinematographer Barry Sonnenfeld (who went on to direct movies himself) seems to be almost throwing his camera around the set (with the Coens, he developed the famous "baby-cam" shots, to show infants-crawling POVs). The film also features some of the most astoundingly madcap dialogue ever, such as when Cage says, "I found myself driving by convenience stores that weren't on the way home."
Robot Monster (1953)
This film stands on its own, but also represents the dark underbelly of cinema: the B-movie. These days, "independent film" is an almost useless label (since Miramax and other once-marginal-now-mainstream studios have made it big business to be called "independent"). But the "B" film has always demonstrated that real people can get into the film business: all you need to make a film is a camera, some film, some friends, a gorilla suit and a diving helmet though the helmet is optional.
The Shining (1980)
If this Stanley Kubrick adaptation of the Stephen King novel was filmed in German rather than English, critics would hail it as an intelligent and endlessly thought-provoking horror film. They should anyway. On a personal note, this film also scared some boys who watched it and many other movies in Vernon's storm shelter a long long time ago.
Swing Time (1936)
I can imagine what you're saying and you're right, the comedic moments are dated and forced. But Fred and Ginger float across the screen and the songs are lovely. Along with Gene Kelley, these two can convince "nonbelievers" to spend a few hours with Hollywood musicals.
This is the one film on this list that's likely to be many other lists appearing at this end-of-the-millennium. This obscenely beautiful nightmare features James Stewart and Kim Novak as the lovers who will never be together. Perhaps Hitchcock's most personal film, it's the one where the villain disappears and you don't even notice. The cinematography is luminous (particularly after the restoration) and Bernard Herrmann's score is perfect and haunting. The closing scene and final shot are stunning; each certainly stands as one of the best in the history of film.