Hey guys! I'm going to start with what I have watched. I watched descendants of the Sun, that winter the wind blows, and healer. All three of them were amazing. I love dramas that will make me cry. I need more of it. But it must also have romance as a big part of it. Action is also good if it can be put in, like in healer. 

That Winter, The Wind Blows is one of my very, very favorites!!! <3333 

Since you liked that one so much, I definitely recommend It's Okay, That's Love -- it has the same main male lead in it.  It's an AMAZING romance drama.

Also recommend these:

The Bridal Mask
Uncontrollably Fond (currently airing, but it'll make you cry...SO GOOD)
W - Two Worlds (also currently airing, but highly recommended)
Another Miss Oh
The Princess' Man
Kill Me, Heal Me
You Who Came From the Stars
Scent of a Woman (definitely cry worthy)
The Master's Sun
The Greatest Love
Marriage Contract
I Hear Your Voice
The Reply series (1997, 1994, 1988)
Beautiful Life - the best I've ever seen
Orange Days - still watching, but giving the above a run for its money
Long Vacation - noona romance with great chemistry and music
Pride - wonderful.  One of Kimura's best imo.  Hockey drama.
Love Generation - pretty good
Master's Sun - overrated imo, but the OST is incredible.  Overall, pretty good.
Fated To Love You - cheesy and stuffed with all the usual cliches, but the male lead is a riot.  Great music too.
In the Mood for Love - a must-watch movie romance.  Follow up with 2046.
Always - movie
Secret - movie
Time Between Dog and Wolf - spy romance
Nana



I would like to suggest you "It's Okay That's Love", my all time fave.

if you want something to make you cry, you need to watch "Dear My Friend".
Actually the main focus is not the romance, but it's still a big part of it (With Jo In Sung here too..)
JDrama:

1 liter of tears
Buzzer Beat
Hana yori dango
Pride
Taiyou no kisetsu
Tatta hitotsu no koi

KDrama:

I'm sorry I love you
Kill me heal me
Marriage not dating
Secret garden
The greatest love
The master's sun
The moon that embraces the sun

Action & romance dramas:
City Hunter
Korean Peninsula