I love any question that gives me the opportunity to dole out recommendations while dispelling popular cinematic myths. What's the beginners guide to the best foreign movies you ask? Conventional categorization would indicate that you're up against quite an endeavor, but that's an (admittedly forgivable) ethnocentric misconception, unless of course you cannot read, in which case this belief becomes stark reality.
Because foreign films are as unlike one another as the American Western and Musical are (alright, Paint Your Wagon, fair enough, now go watch Sholay) and the only common thread between them are those pesky plagues of movie-goers everywhere, subtitles (but even then, not always). Regardless of whether you watch movies strictly for mindless escapism, or seek out the emotional, intellectual and sensory overloads that cinema can offer, the best foreign movies can satisfy your expectations while expanding your horizons, the only requirement being that you check any reservations about reading at the door. Subtitles seem daunting at first, but you'll get used to it, I know because you're sharp and open-minded (would you be asking this question if you weren't?).
Beyond that, there's nothing to stop you, but now that you've marched into this sprawling, exotic smorgasbord, you understandably would appreciate some recommendation. Best is a loaded word, but some films, directors and even entire movements should be experienced before others. Cinema is all about the gateway drugs, and you've got to build the right foundation before it can elevate you to levels you never even imagined. There's no one magic foreign film to start with.
The first two that hooked me were Jean-Pierre Jeunet's whimsical romance Amelie and Fritz Lang's science fiction masterpiece Metropolis. The later film is also silent, but the substitution of subtitles for title cards neither changes the point nor ultimately matters here. Both are highly stylized genre pieces that are respectively joyous and awe-inspiring, and both go down like fine French wine (or a strong German beer). They surely ignited something in me, and to this day I can still enthusiastically recommend them.
Initial impressions are important though, and it makes sense for your first foray into foreign film to be in a genre you have a predisposition for. One of the classic foreign genres we think of here is the Samurai Film, and the canonized cinematic saint of feudal Japan is Akira Kurosawa. You've probably heard of The Seven Samurai, and what a terrific start that would be, provided you're up for the epic length. I would personally suggest starting with his more concise Rashomon, or his stunning adaptation of Shakespeare's MacBeth, Throne of Blood. The other staple of Japanese cinema is anime, and if you have any preconceptions of this label, I would point you to Hayao Miyazaki's Spirited Away, a wondrous film for children and adults alike that is proof positive that animated films can be great movies too.
Moving slowly westward, it's hard to pass up the martial arts extravaganzas of Hong Kong and China. The manic comedy Peking Opera Blues is my personal favorite, but Kill Bill fans should take a liking to The 36 Temples of Shaolin and it's easy to fall under the gorgeous sway of Hero or Crouching Tiger, Hidden Dragon. India of course has Bollywood, which must be experienced to be fully understood (and experienced again and again to be appreciated), but some excellent introductions to their everything and the kitchen sink approach include Lagaan, Diwale Dulhania le Jayenge, and the aforementioned musical western, Sholay.
Soviet history is chock-full of amazing films, but they tend to weigh heavily on you (Stalker is trying, but majestic) and the one you're likely to see come up again and again is The Battleship Potemkin. My verdict is that it's an important film, one that should be seen eventually, but not one to take in at the outset. If you're looking for something that'll leave you floored, if not exactly on the edge of your seat, I suggest Russian Ark. It's essentially a tour of Russian history from within the confines of The Hermitage, but filmed in a single, mind-blowing, tracking shot. That's right, an entire movie filmed in one fluid shot. The film may only be 90 minutes, but that's epic.
There's also the wealth of European art films which get tossed around on all-time greatest lists and are bound to come up as you begin investigating. Of the best known titles, I enthusiastically recommend The Seventh Seal, a very accessible introduction to the spiritually conflicted world of Swedish auteur Ingmar Bergman, and the source of every playing chess with death reference you've ever seen.
From Germany, there's the fearless pre-noir M (also by Fritz Lang) which memorably serves as Peter Lorre's screen debut, and if you're not one easily hampered by budgetary confines, Werner Herzog's Aguirre: The Wrath of God is a bold and harrowing excursion into the wilds of South America following a conquistador's doomed quest for El Dorado. Spain I can't mention without citing the colorful melodramas of Pedro Almodovar, and two of his collaborations with Penelope Cruz, All About My Mother and Volver, would make excellent starting points. There's also Pan's Labyrinth, an especially thrilling fantasy that is so rich it could probably be enjoyed with the subtitles off.
France and Italy have much to offer too. My first Italian film was by reputation the greatest of all, Federico Fellini's 8 1/2, which despite its rapid-fire pace and often confusing interludes, is such a stylish and high energy film that it is easily enjoyable, if not entirely comprehensible, to beginner enthusiasts. There's also a rich collection of Italian thrillers and horror, many of which fall into a highly specific genre known as Giallo, which are must-sees for any horror fanatic. My favorite horror film of all time is Dario Argento's Suspiria, and you'll understand in the first 10 minutes why.
Speaking of horror, there's a supremely eerie French film called Eyes Without a Face that surely ranks among the best of the genre also. Other French films to add to your netflix queue include Francois Truffaut's legendary love-triangle, Jules & Jim; Luis Bunuel's surrealistic masterpiece, The Discreet Charm of the Bourgeoisie, and the nail-biting adventure The Wages of Fear, about truck drivers transporting nitroglycerin across dangerous mountain roads.
I realize I've ignored innumerable films that would make equally great starting points. I haven't mentioned Korea (monster movie fans, watch The Host), Mexico (Y Tu Mama, Tambien is the standard, no?), the booming film industry of Iran (Offside is an eye-opening place to start) or the oddly prolific boom in 1960s Czechoslovakia (Daisies for the adventurous sort, Closely Watched Trains for the rest). The good news is I also love listing, so followup questions that demand a ranking of sorts will be met with equal fervor. In the meantime though, you have some watching ahead of you, and frankly, so do I.