I just the original Oldboy for the first time about a month ago, and just saw the Spike Lee remake yesterday. In a lot of ways it illustrates the differences between how stories are told in both cultures. The remake was much more modernized, no eating of live squid, just postickers, none of the hero acting like a dog. The new one was good, but it was missing all of the dark comedy elements of the original. Like when the hero breaks into the bad guy's lair and starts killing dudes, and then is told by a bodyguard "You could have just talked." Forgive me for the cultural generalization, but I find Oldboy (and the excellent other entries in that trilogy) a very detailed story of obsessive revenge. Maybe Korean culture has more of a sense of it than American films, but the remake didn't dig as deeply into the psychological elements surrounding revenge. It's made me realize in a lot of American films, revenge is just about expressing anger. But something like Oldboy made me consider the psychological cost of harboring revenge.
As another example, the scene where the hero was confronted by over a dozen bad guys and a huge fight broke out. The remake was choreographed really well. The original fight was much realistic and more brutal in terms of damage dealt to the hero. I prefer the original for its quirkiness, but I'd probably recommend the remake to most Americans. Also if a person is not used to reading subtitles, foreign films can be really hard to digest, and dubbed movies often lose the nuances of the actor's performance.
I like watching movies with the sound down. A good film you should be able to tell how the characters are feeling by watching them. Even a foreign film you can tell from tone of voice how people feel.
Here's some foreign films I've checked out this year:
Enter The Void - this one is haunting me. French film but in English so no dubbing/subtitles to deal with. Equal parts drug s, sex, and the death experience.
Irreversible - by same director, even more haunting. Unless you can steel your emotions against attack, avoid this at all costs. It is completely brutal. Story told in reverse like Memento.
Lady Vengeance/Sympathy for Mr. Vengeance - other parts of the trilogy that Oldboy belongs to. Neither quite as good as Oldboy, but Sympathy comes closest.
Madrid 1987. Man and woman locked in bathroom for most of movie. More intersting than it sounds.
Bedevilled - I think this one was Malasian, another revenge story of a woman trying to escape an abusive marriage.
The Coffin - Couple participates in Buddhist ritual of sleeping inside a coffin to erase bad karma. Pretty good, but didn't run with the concept the way I'd hoped.
El Mariachi - Love Robert Rodriguez', just missed this indie gem.
Ip Man series, Crouching Tiger, Shaw Bros., many many martial arts movies. Enjoying fantasy is a pre-requisite to most of these. The Ip Man material is much more realistic.
Battle Royal - kids made to fight to death in remote location. Think Japanese Hunger Games.
Story of Ricki - personal fave, so ridiculous with low-budget over-the-top martial arts gore.
The Housemaid - excellent Korean flick about power dynamics as a maid wedges herself in between a husband and wife.
Ju-On 1 and Ju-On 2. You may have seen them remade as The Grudge. The originals are creepier.
Kidnapped - Spanish film dubbed in English. Similar to Funny Games but more graphic. Would have preferred subtitles, but still a decent movie.
Funny Games - original German version. Haven't seen the remake but would be surprised if it is as good.
Audition - Japanese film about a widower opening an ad looking for a new wife. But his choice might not be as perfect as appears. This one has some horror scenes late in the film that are seared into my brain. Really good film.
Ichi the Killer - infamous Japanese movie.
Strange Circus. Bizarre Japanese movie with plenty of perversion and quite a shocker at the end.
Dumplings - Just how far will some Chinese women go to retain a youthful appearance? A strong performance from the odd and alluring Bai Ling.
I Saw The Devil - guessed I'm biased, but yet another Korean horror flick that gets high marks from the syrup-meister. Theme? You guessed it. Revenge. I found the late parts of the film distressing, which I suppose any good horror film should do.
End Call - high school girls discover Satan's cell phone number and call to make their deals with the devil.
Only God Forgives. In English, but set in Thailand. Has some odd acting, but the cinematography was just gorgeous.
There's more, but that's what I recall at the moment. I want to get into more mainstream foreign movies, because my taste is biased towards horror
Edit:
@sasNW I added a few more.