The movies I will recommend will not be ranked and will not be sorted either alphabetical or by any manner.
Also those movies I present in this post are recommended but not for all, some are at least weird, and you are advised that some of them will test your senses and your ethics, your stomach, and more one at a movie or all together.
Memories of a Murder

Two detectives trying to solve the mystery behind the identity of the serial killer. Under different methods, a violent one, first shoot then ask questions, and a more methodical educated one, one that trust more the facts than his feelings.
rating from imdb
Premonition (Yogen)
Do not be mislead, this one has nothing to do with the 2007 film under the same title, staring Sandra Bullock

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Battle Royal

"At the dawn of the millennium, the nation collapsed. At fifteen percent unemployment, ten million were out of work. 800,000 students boycotted school. The adults lost confidence, and fearing the youth, eventually passed the Millennium Educational Reform Act - AKA: The BR Act..."rating from imdb
House of the Flying Daggers
rating from imdbThe film is set in 859 AD. The once great Tang Dynasty is now in decline. Numerous rebel groups have formed, the largest of which is the House of Flying Daggers, based in Feng Tian county. The Flying Daggers steal from the rich and give to the poor, gaining the support of the locals.
The local deputies have managed to kill the leader of the Flying Daggers, but the rebel group only becomes stronger, due to a mysterious new leader. Jin and Leo, two police captains, are ordered to kill the new leader within ten days.
Hana-Bi

Kitano plays Nishi, a violent and unpredictable ex-police detective who quits the force after a terrible incident that results in his partner, Horibe (Ren Osugi), being confined to a wheelchair. After his retirement he spends much of his time looking after his wife Miyuki (Kayoko Kishimoto), who has leukemia....and one usufull information, hana means flower, bi means fire, all together fireworks, literally fireflower...
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A Cruel Attendance

The story as far as I recall is about two losers, who own money to yakuza(?), try to get some money by kidnapping rich people's children. But, they never get it right...
rating from imdb (I would give it a 6,5+)
Save the Green Planet

...and the plot is even more twisted:
A young a man who believes that aliens are about to attack Earth and that he is the only one who can prevent them. With his childlike circus performer girlfriend, he kidnaps a powerful executive who he believes is a top ranking extraterrestrial who can contact the prince of these aliens when the upcoming eclipse occurs. After imprisoning him in his workshop/basement he proceeds to torture the executive, and slowly Byeong-gu's true intentions are revealed.rating from imdb
This one I've seen it back in 2004, at Athens movie festival called "nights of premiere"(I don't even know if the translation is good) alone in a full cinema after midnight. I believe, judging from the expression of the attendants that most of the people enjoyed it!!!
Kung-Fu Hustle

rating from imdb
I sincerely thank - m - for her corrections, Kung-fu hustle is Chinese.
Emperor And The Assassin

rating from imdb