Apologies for echoing other posters (but they are bang on the money), but you the Vengeance trilogy (Sympathy for Mr Vengeance, Oldboy, Lady Vengeance) are probably exactly what you're looking for. The same director did an unusual vampire flick called 'Thirst', didn't get much attention but I thought it was brutal and brilliant.
Other stuff from Korea:
I saw the Devil (really, truly ultra violent)
The Chaser
Memories of Murder
A Tale of Two Sisters
Brotherhood of War
Japan:
I liked Battle Royale too. Try 'Confessions'. Similar themes, and a very stylish film. I second the reccomendation for the Seven Samurai, the fight scenes look a little tame by today's standard but if the characters and story click with you, then it's a film you will never tire of seeing. Also worth seeing by the same director is Yojimbo, the inspiration for a Fistfull Of Dollars. Most of his films are pretty fucking amazing to tell the truth. About thirty years later he dropped two gigantic historical Samurai war films, Kagemusha and Ran. They are heavy duty stuff, massive, massive battles and serious stories. Kagemusha is definitely worth seeing, the story is more likely to take you.
A more modern take on the samurai film is '13 Assassins'. It's complete mayhem, a bloody nightmare. Brilliant stuff. The guy who directed it Takeshi Miike is the Balotelli of Cinema, you never know what you are going to get, only that it will be something you've never seen before. He has a nice line in twisted thrillers similar to the vengeance trilogy. Check out 'Audition'.
Still in Japan, one gangster flick I really, really like is 'Sonantine'. Very off beat. The lead character is played by the school teacher from Battle Royal. He also directs this. His name is Takeshi Kitano. Takeshi of Takeshi's castle, believe it or not. As you may have gathered he's another wild-card, he's directed loads of interesting films.
I don't know much about John Woo stuff, he's very well loved though. Other stuff from Hong Kong to check out:
"Infernal Affairs" 1 & 2 (the first of which was remade shot-for-shot as the DiCaprio-Scorcese film "The Departed). Very gritty and exciting.
"Election" Yet another crime flick, but really interesting. Be warned, the English speaking parts are completely laughable.
Away from Asia;
Russia: "Come and See" (Idi i Smotri) is almost certainly the best war film you've never seen. "Stalker" is not a thriller / serial killer flick, it's a very strange sci-fi movie.
France: La Haine, The City of Lost Children, Nikita, A Very Long Engagement, Brotherhood of the Wolf, The Disappearance.
I think most of the other clear choices have been done, Millenium Trilogy, Hero, Crouching Tiger, and so on.
A few more top class horror stories, apologies for any dupes; "Deep Red", "Let The Right One In", "Chronos"
Have fun.