First off, if you're going to get into Korean Cinema you need to be aware of one Park Chan-Wook (or Chan-Wook Park, I'm not quite sure which way round that should be).
Probably most famous for his vengeance trilogy:
Sympathy for Mr Vengeance
In an interview I saw with him he admitted that he never intended to make a trilogy, but during and interview with the Korean press during the release of Oldboy, somebody asked what his preoccupation with vengeance was about, he replied I'm just making the three vengeance films then leaving the subject alone. At that point he realised he'd only made two, so the third was made to save face.