Densha Otoko
My Name is Kim Sam Soon
Secret - starring Hwang Jung Eum
It's Okay, That's Love
I think I've cried while watching lots of dramas but the ones that had be bawling like the stuff was happening to me, I was crying while making noises, had a headache, running nose and other serious crying symptoms were;
49 days
1 litre of tears
The hours of my life
Gotta say 1 Litre of Tears too. I often cry while watching dramas, but nothing has been as bad as that one.
I don't tend to like melodramas (watching actors cry constantly just makes me angry rather than sad) but a few dramas have really made me cry.  two episodes of Fated to Love You were hard to watch because I was crying so much.  I really loved the characters and it hurt me to see them suffering.  Also one episode of Moon Lovers made me cry, I had to pause and take a break.  Most of Baek Hee Has Returned (3 out of 4 episodes) made me laugh out loud but the 3rd episode had me crying my eyes out.
1. 1 litre of tears.. from episode 3 until the end I cried like an idiot.. :)

2. Chuno.

3.Stairway to Heaven
1 Litre Of Tears
Mirror Of The Witch
Moon Lovers: Scarlet Heart Ryeo
The Master's Sun
Faith

... just to name a few that really got to me
The first one that comes to my mind is Marriage Contract. I cried through every episode. 
49 Days
I went through approximately one tissue box, one lotion bottle, and one chap stick.
Mother, 1 Litre no Namida, Kamisama Mou Sukoshi Dake, Woman.
my sunshine
Good Doctor 
King2Hearts
Autumn Concerto
Legend Of the Blue Sea Merman Episode
Werewolf Boy Movie 
secret
Scarlet Heart  I & II
Scarlet Heart Ryeo
Boss & Me when they killed Huang Ming's character and when king & his wife been killed
Fated to Love You Both K & TW versions
My Love Eun Dong  
the Year of Happiness and Love  ( cried my eyes out when he had to marry another girl and the other girl had an amnesia as she could not handle the stress - pain, she fell pregnant  and eventually main guy dies from brain aneurysm)
Faith 
East of Eden --- a melodrama w/out the cliches and w/ an intriguing story line! .... Well-developed characters w/ Realistic thouhtful Character Developement.
Ouroboros
Angry Mom

These are the only dramas I have legitimately cried over.
I don't cry much over dramas except when I can really relate to the scene so I cried over High School Love On when Shin Woohyun's grandmother passed away and cried over Fated To Love You when Miyoung lost her child during an accident.