Hmmm probably for me it would be mostly the ones who had tragic/unhappy (for the couple or main hero) ends. Um. Spoiler-ish? XD
Ok, dramas that truly moved my emotions:
The Moon that Embraces the Sun - totally felt along with the main couple
Cruel City - left me with tears T_T
Mirror of the Witch - still am bittersweet
Scholar Who Walks the Night - teary 'cuz of Gwi
King's Daughter, Soo Baek Hyang - sort of? well, I definitely cheered for Solnan and still do
and currently: W - Two Worlds - it's left me a complete mess, in a good way. It's a miracle I'm not floating around with all the excitement :D