For me , it's hands down Choi Ji Woo in Stairway to Heaven. 
I can't think of any at the moment but @Kristana, I agree that Kim Soo Hyun in Moon Embracing the Sun was great. I feel like this thread might need another version of worst criers, lol.
Prince Wang Wook played by Kang Ha Neul in Moon Lovers: Scarlet Heart Ryeo (2016). It's heart wrenching to see Prince Wook cry after the death of his wife Lady Hae.
Jo In Sung. Son Ye Jin.
Lee Jong Suk
Lee Jun Ki
Park Shin Hye
park shin hye [in miracle in cell no 7 ..her crying scenes are so natural]
I'm finding it hard to choose a single person so i'm going to just list the few that first came to mind;


[1] I'm not even going to try and hide my bias but as you can see from my profile pic I have to choose Ji Chang Wook. If anyone has seen his performance in Empress Ki than i think you can probably agree with me. 

[2] Kang Ha Neul as Wang Wook in Moon Lovers.

[3] Lee Joon Gi as Wang So in Moon Lovers

[4] Hwang Jung Eum as Kang Yoo Jung in Secret.
Just wanna add this scene too. T_T

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Yeo Jingoo gives me these feels
Park Shin Hye is good at it, but Lee Yoo Ri is by far he queen of crying in korea.  She's even known for it.  Just watch any drama she's ever been in.
I don't remember all dramas crying scenes but all the actors/actresses did great in "I Hear Your Voice" I felt like crying with them T_T
I found Kim Go Eun's crying scenes in Goblin to be very touching. Even her sobbing seemed so real to me. In fact, I didn't like her that much during the first episodes because her facial expressions and the way she spoke were kind of put on at times. But when the plot got more complex and so her role, she really surprised me. She proved so much sensibility during the sad scenes. I'm definitely going to check her out in more serious roles.
Park Bo Young  ( Strong Woman Do Bong Soon )
Park Shin Hye 
Kim Go Eun 
Gong Hyo Jin