For me, 1st is 49 Days, since it was the first kdrama i ever watched, that made the trauma worse.
Then Healer is my all time favorite, cuz it brings all the emotions ever, its a full ride.
Glass Mask. I feel like a train wreck every time i watch it. I need a Masumi in my life ( jk).
School 2013
King 2 Hearts
Reply 1997
Bridal Mask
Reply 1988!!! Bridal Mask too..
I mean I just rewatched Boys Over Flowers (The Korean Versions) and it literally destroyed my emotions.
Kill me heal me, reply 1988
Its Okay thats Love MESSED ME UP SO BAD!!!!! 
The love triangle in Damo tore me apart from the inside.

Also, with Reply 1988 I empathized so much with every single character... I felt just as if they were part of my own family or group of friends. I laughed and cried with their stories. I can't even watch Jung Hwan's scenes anymore because it makes me feel sad everytime I do. 
So far for me it's actually been Uncontrollably Fond. I know so many people have given up on this drama but it get's much better as the drama progresses & Kim Woo-Bin's acting is killing me. The last episode had me all curled up on my couch near to tears & let me tell you I can name on hand the things that have made me cry. 
Missing You
Good Doctor
I Remember You
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
Cruel City definitely.
Jam Loey Rak
Kill Me, Heal Me
Long Love Letter
Mother (J)
Tenno no Ryoriban
Ouroboros
Tonbi
Hong Gil Dong