I prefer new quality video, but "older" versions are of course okay. Trying to avoid deathly sickness plot hehe.

I am really loving I Miss You, since I've read it somewhere in this recs thread. It was exactly what I'm looking for. Funny moments in the show are okay, to balance things out., but I prefer more sad moments & good plot with a touch of comedy. More sad moments > Funny moments

For newer stuff I would suggest 

49 Days
Secret
Innocent Man
Bad Guy
Fated To love You


But there are also some good 'Oldies' that will have you reaching for the tissues such as 

Sorrry, I Love you
Bad Love
Summer Scent
secret , mask , innocent man , golden rainbow 
King of Baking Kim Tak Gu, Triangle, Shining Inheritance, Bridal Mask, Doctor Stranger, Tree of Heaven. Those are all melos that I really enjoyed. 
Your new to drama land! Welcome!

I love sad dramas. Here are my favorites~
(This list is in order from best dramas to worst, though none of them are bad. Numbers are tearjerker ratings 1-5. 5 being most tears)

2 It's Okay, That's Love- It's sad through out but only a few tears for this one. 
4 Cruel City- The drama is about the underground. Cry at the beginning, cry in the middle, and cry in the end. The emotions are super high.
5 Ouroboros- My all time favorite Japanese Drama. Check it out :)
5 49 Days- It's a weepy one. Definetly one of the saddest dramas out there. 
5 Mama- Winner for tearjerking. I cried the entire time. Seriously. I just didn't stop, through all 24 episodes.
4 Scent of a Woman- while it is meant to be sad, its also meant to be happy, and it melds the two rather well.
2 Secret Garden- This has one of my all time favorite sad scenes. 
4 Super Daddy Yeol- It was cute, and decent. Watch the others first!!

Also I don't think Innocent Man is all that sad, BUT it is my all time favorite drama, you should definitely watch it!

If you need more just message me! I'm always on MDL :)

Autumn's Concerto
Buzzer Beat
Can You Hear My Heart
Innocent Man
Kill Me, Heal Me
May Queen
Padam Padam
second 1 Liter Tears - it makes you cry like every episode but it's about sickness
What Happened In Bali - it's sad/depressing and made me cry on the last episode-twice since I re watched it.
Que Sera Sera
I am really sad that no one mentioned those:-
1-Shark >>>The masterpiece 
2-A love to kill >>>The awesomeness 
3-Flowers for my life >>>funny, sad but that kind of sadness that makes you tear and smile at the same moment
4-Padam Padam

for less sad
1-In time with you
2-Innocent man
3-What happened to my family? >>>this is very heartwarming 

Enjoy :-)
Proposal Daisakusen << my favorite

90 Days of Love << this is 6.6 but probably cuz its about first cousins and death so maybe not

Sang Doo, Let's Go To School
Delightful Girl, Choon Hyang
Full House
Full House thai version

Rent a Girlfriend Home for New Year << not 100% sure about this
Save the Last Dance for Me

Hormones/Hormones 2 << this show is more realistic so it has some sad moments
Since you mentioned I Miss You then I assumed the romance had to play a big part? Then:

Kdrama:
Will It Snow for Christmas?
I'm Sorry I Love You
Thank You
Let's Go to School, Sang Do!
Beyond the Clouds
Secret
49 Days
Sad Love Story

Jdrama:
Bara no nai hanaya
Nagareboshi
A Hundred Stars Falling from Sky
Crying out Love, in the Center of the World

Have little romance but it got something that'll make you feel sadness almost in every episode (and since I've been trying to recommend them in every chance I got) :
Battle of Changsha
Soredemo Ikite Yuku

I'm a bit all over the place when it comes to dramas so i'll recommend some of my fav's from each country:

Korean:
I Hear Your Voice - is one of my favorites that mixes comedy and really heavy moments well. You'll laugh just as much as you'll cry. I was doing both at the same time by the end!
Secret - The only TRUE melodrama I've seen that has left me speechless
Thank You - Nothing but tears as it involves a cute sick child ;'-(

Japanese:
Koizora - There's a drama and a series, I've seen both and you really can't go wrong either way

China:
Scarlet Heart - Historical tearjerker. Oh the feels

Taiwan: Summer's Desire - it's 2 hours per episode with a total of 14 episodes.It involves a twisted love triangle, so depending on who you're rooting for you can love it or hate it.
I am honestly checking each one out and their all seems interesting and will deliver. Normally, if 7 mins of first eps is soo boring I stop and check others. Sorry for being shallow. For instance Padam Padam, I have high expectations, but the trailer and episode 1 was too boring that I couldn't really continue even if I want to. 


I'll try the others and will update if I've picked my "priority" list



Thank you!
Have you seen 'Sad love story'? It's my fav drama of all time, and well, the title says it all :) It's from 2005 so it's pretty old, but it's definitely worth the watch!!!
The snow queen is heartbreaking and the storyline is so beautiful.