I only remember crying (or well.. tearing up a little) with You're Beautiful and Page Turner.
You're Beautiful because it was the first drama I finished and my favorite at the time, and Page Turner because it's just really sad.

And also a little bit with Sassy Go Go when the role Ji Soo played got beat up by his dad, since he is my favorite actor, it was just sad to see :(
Koizora
Weightlifting Fairy Kim BokJoo (I binged watched the drama, was so happy for them. When I finished it I was just so sad because I wanted more!)

As for movies:
Sunny (I've seen it something like 10 times but I always cry for half an hour!)
Our Times (Same, I've seen it the same amount as Sunny and almost always cry)

There were a lot more dramas and movies that made me cry, but those are the ones that I preferred! :)
I might be weak but I just recently cried 3 times in 1 episode from watching Ruler : Master of the Mask. As for which drama I cried the most. I did cry during uncontrollably fond. I honestly can't remember when I had it the worst. I cry a lot watching dramas. I think the worst was actually a web drama called star of the universe.. LMAO.. I've cried watching Journey of Flower,Nirvana in Fire, Uncontrollably Fond, Eternal Love, The Imperial Doctress, The Princess Weiyoung, Love me if you dare, Goblin... I cried watching so much stuff.  
TheGrowlingStomach: boss & Me (but not because of the story, I just cried because of how badly the main male lead killed the drama for me.)

me too. just thinking about the male lead makes me want to cry out of anger.

1 litre of tears - every episode. It was an ugly sight
reply 1988 - superb acting and writing. I teared up a few times
hong gil dong - the ending...


I'm sorry, I love you