I've cried more watching Movies than Dramas
Pandora, Sunflower, Man from Nowhere, My Way, Flu, Train to busan. (All of which I highly reccomend)
As for dramas; Wise Prison Life, Black. (Not overwhelmingly sad but definitely has it's moments.) There are others but can't really remember atm.
Oh and probably Boys over flower back in those innocent early teenage years watching my first ever kdrama where I'd cry over the TV for my Gu Jun Pyo hahahahhaha.. oh how naiive :')