I am a big Korean film buff. Lots of good ones listed here. I saw a mention of New World which is one of the most intense films I've ever seen. Between that film, A Bittersweet Life and A Company Man, 70% of Korea's male population must be dead. If you like gangster films, Don Lee is in a ton of them. He plays the same guy in every movie but he plays it really well and they're always entertaining
If you like drama/suspense. Joint Security Area is great and The Berlin File is really good (spy stuff). The Thieves is entertaining as well (Ocean's 11 type movie). The Brotherhood of War is pretty great (Korean war)
Twenty is a decent comedy about guys trying to lose their virginity and if you can find Welcome to Waikiki, that's the funniest k drama I've ever seen. Season 1 is better than season 2 but the ongoing saga of Rebecca the car kills me
Koreans also do the best melodrama out there so if you can find Ode to My Father, that is fantastic. More Than Blue is the saddest movie I've ever seen. Sunny is phenomenal. There are some great romance dramas that aren't cheesy like The Classic, My Sassy Girl (anything with Jun Ji-hyun is typically really good like Il Mare and Windstruck), A Moment to Remember, Christmas in August...
If you like k dramas at all, there are too many great ones to mention but Netflix should still have Live, about rookie cops in Seoul and Misaeng, which convinced me to never ever work for a Korean company. They just dropped Reply 1997 which is an all time great IMO. There are dozens of great dramas though