Some good older dramas:
k-dramas - 49 Days, City Hunter, The Bridal Mask, The greatest love, Cruel City, Queen Inhyun's man, Coffee Prince, The princess' man, Scent of a woman, Flower boy next door
c-dramas/tw dramas - Autumn's concerto, It started with a kiss (and the sequel They kissed again)
j-drama: hotaru no hikari, hana yori dango (both seasons)
More recent dramas:
action/thriller - Black, Catch the ghost, He is psychometric, Hello monster, Rookie Agent Rouge, Stranger, The guardians
modern romance - A love so beautiful, Chicago Typewriter, Le Coup de foudre, Marriage not dating, My sunshine, Just between lovers, sassy go go, 30 but 17, star of the universe
historical/fantasy romance - Bloody romance, Goodbye my princess, Love and Redemption, Love of thousand years, Mr Sunshine, Queen for 7 days, The journey of flower, the promise of tiger and rose, The scholar who walks the night, the sleepless princess