oldboy (2003)

aka Oldeuboi. Old Boy.
"Remember this: "Be it a rock or a grain of sand, in water they sink as the same."
Dae-su Oh (Min-sik Choi) manages to break out of solitary confinement after being kidnapped and imprisoned for 15 years, with no explanation. So no wonder he is after answers, but finds that he only has 5 days to find his jailer.
Original, shocking and captivating (no pun intended).

i'm a cyborg, but that's ok (2006)

aka Saibogujiman kwenchana.
"If only I had one reason for existance..."
Young-goon (Su-jeong Lim) is sent to a mental hospital, as she believes she is a cyborg, and plugging herself into the main's didn't do her much good. There she meets and falls for Il-sun (Rain), another patient, who spends his time playing table tennis, but can he get her over her fixation that cyborgs don't eat, before she dies of Malnutrition.
A quirky romantic comedy, directed with hyperreal verve by Park Chan-Wook.

thirst (2009)

AKA Bakjwi. Kawaki.
"Those who seek direct communication with God are prone to self-hatred."
Sang-hyeon (Kang-ho Song) is a priest, dedicated to helping others, who volunteers for a secret vaccine project trying to eradicate a deadly virus. Complications ensue and the priest dies following a blood transfusion, but then miraculously revived, he re-enters society as a fated miracle worker. He stays with a friend he has cured of cancer, and it is there that he starts to struggle with new found desires. Especially when he starts to be attracted to the friends wife Tae-ju (Ok-bin Kim) and he descends into a world of sensual pleasures craving blood.
Visually and viscerally stunning horror.