Except for Audition, all the good foreign films I watched were available on VHS, back when the wheel was first being applied to tape reels and video fuzz was a bonus feature. My five favorites are very different from one another, but except for Audition I would gladly watch each one again.

1. Betty Blue. Beatrice Dalle is one of the most beautiful people to ever grace a film. Betty Blue is the story of two zero-sum, working-class lovers, Betty and Zorg, who begin the movie in the sun-baked clutches of a slumlord. Betty's smoldering temper and love for Zorg gets the better of her, and they make an incendiary exit. The couple tries to revive Zorg's handwritten novel in the second third of the movie, but Betty, despite the enmeshing of her life with Zorg's, begins to yield to personal demons more and more in one of the saddest progressions I've watched on film. The ending, while a little ludicrous, recovers after a silly wobble, and says: life goes on; all you can do is your best. A few scenes have been removed from later American versions, so it's worth it to find a vintage French version. One of the deleted scenes, where Betty and Zorg bury their tensions to watch the sun set in front of their new little home, is a timeless triumph and embodiment of romance.
2. Run Lola Run. If the 1990s could be distilled into a single work, it would likely be this one. The hyperkinetic story of a German woman making frantic attempts to raise money before her boyfriend is rubbed out by criminals, the cinematography and pacing are visual espresso as powerful as Lola's flaming red hair. The humor is dark, the language pithy, the acting sharp. A Gen-X gem.
3. Audition. Japanese society was once known for the suppressive roles it gave women. This movie is a primal scream that shakes these antiquated notions to dust. What makes this film unforgettable is the immersiveness of the writing and filmmaking. Even though it has sequences as horrific as Jacob's Ladder, and worse, the progression of the film's first half is smooth as the side of an old-fashioned razor. But then director Takashi Miike turns that razor on its edge and swings it in wide arcs at the viewer in the flash of an eye. It was so realistic and horrifying, with solidly established characters dropping straight down into madness, I almost passed out, and I've been able to watch a lot without batting an eyelid. Not recommended for anyone with a weak stomach, but if you like your movies brutally realistic, Audition is for you.
4. Metropolis, 1984 Giorgio Moroder restoration. Moroder breathes life and hue into this tale of class struggle and the dangers of technology. Featuring a cold industrialist father, his idealistic son, an enlightened teacher turned labor movement leader, a mad scientist, a femme fatale robot, and a bear of a foreman, the archetypes and themes still resound through 2008. The stunts are death-defying, the fragmented storyline lovingly restored (Fritz Lang's movie was heavily edited for its American release), and the soundtrack is a marvelous collection of early 80s rock.
5. Delicatessen. A story set in a post-disaster France in the 1950s, this movie is a campy, slow-paced thriller about a homely man who moves into a butcher's apartment building, charms his landlord's daughter, and finds himself heading the way of the previous tenant, who disappeared under mysterious circumstances. A grimly funny take on "meat is murder", the film features a trio of vegetarian resistance fighters (les Troglodytes) and an intriguing plot twist in the form of a knickknack called "The Australian". The leading man gives great hope to those homely with romantic aspirations, and the climactic confrontation is a unique tribute to love in the time of mortal danger. Very weird, but certain to kick around your thoughts for some time.

These are my favorite foreign movies. While I've seen a few others, none of them have stayed in my mind like these. I hope you are able to watch and enjoy at least one of these sometime.