My top ten Korean dramas: (not in particular order) 
it's ok that's love
the masters sun
six flying dragons
i am sorry I love you
my love from other star
signal
i can hear your voice
the greatest love
secret love affair
descendants of the sun / cruel city ( I just started few episodes of cruel city ,so no final verdict yet- liking it so far)

Japanese dramas - not enough for top ten as I have watched only a couple:
1 liter of tears
nodame cantible 
GTO
beach boys
Dr Jin
If you're interested in rom coms or rom--  
in addition to the ones that many have already mentioned…
to avoid repetition…  
(in absolutely no particular order):

- mars (taiwan version) (there is a new japanese version)
- last cinderella
- bromance
- devil beside you
- why why love
- calling for love
- down with love (taiwan) 
- faith 
- king2hearts
- kiss me (thai version) (there are taiwanese, korean, and japanese versions)
- mary stayed out all night
- my princess (korea)
- my splendid life (chinese/taiwanese version) (there is a korean version too)
- oh my lady
- ToGetHer
- you're beautiful (korean version) (there is a taiwanese version too)
- 5-ji kara 9-ji made
- fated to love you (taiwanese version) (there is a korean version)
- flower boy ramen shop
- full house (thai version) (there is a korean version)
- pride (japan)
- prince of lan ling
- rock 'n' road (taiwan)
- that winter, the wind blows
- always (korean movie)
- house of flying daggers (chinese movie)
- my queen (taiwan)

it seems to me that newer shows tend to have higher ratings by significantly more voters/users.  
older shows have already been viewed half to over a decade ago when the majority of the viewers watched these on TV.  
comparing scripts, story lines, production, filming and sound quality, custom designs, general style, etc from 7-12 years ago to today's productions (e.g. less than 5-year-old)  is like comparing apples vs oranges vs watermelons...
 
good luck and have fun!
1. Healer
2. Another Miss Oh

In no particular order :

Splash Splash Love
You who came from the star
Dear My friends
Sungkyungkwan Scandal
Kill Me, Heal Me'
It's Ok, that's Love
Remember : War of Son
1 litre of Tears
1. Healer
2. Another Miss Oh

In no particular order :

Splash Splash Love
You who came from the star
Dear My friends
Sungkyungkwan Scandal
Kill Me, Heal Me'
It's Ok, that's Love
Remember : War of Son
1 litre of Tears
Here's my Favourites List. There's more than 10 but you can just stop there.

It changes every now and then
Not best by any means, just what I personally like best (Generally I'm not into serious, angsty drama, not a fan of Japanese drama)

In no particular order:
1.My Girl
2.You're Beautiful
3.The Greatest Love
4.Coffee Prince
5.Healer
6.Sungkyunkwan Scandal
7.Secret Garden
8.Descendants of The Sun
9.Queen Seon Duk (Period, this one is more serious than most on my list)
10.Nirvana In Fire (Chinese. Very well made imo. This one is not romance, though)

W-Two Worlds is still airing, and unless the drama somehow manages to go crazy wrong, it's definitely up there with my top favorites.

LOVED the Taiwanese version of F4 (Meteor Garden) but it was so long ago so I'm not sure how I'd feel about it if I watched it now. Meteor Garden was crazy awesome, but Meteor Garden 2 was hard to watch. Too depressing/angsty.

Honorable mention:Cheese In The Trap (at first I was ready to put this drama on the TOP pedestal but then second half of this drama just went downhill.)
I haven't seen many, so in no particular order,
  • Boss & Me
  • My Girlfriend is a Gumiho
  • City Hunter
  • Devil Beside You
  • Duang Jai Akkanee
  • Boys Over Flowers
  • Full House (Thai Version)
  • Fated To Love You (Taiwanese)
  • Secret Garden
  • I Hear Your Voice
my top 10 right now, at this moment 

1. Boys Over Flowers
2. Autumn Concerto
3. Princess Pearl
4. Autumn Tale
5. Love o2o
6. Liar Game (jp)
7. Cruel City
8. My Bratty Princess
9. Mars
10. Summer's Desire

The Snow Queen,...
I'll edit later if it changes.

1. Signal
2. I Hear Your Voice
3. Sungkyunkwan Scandal
4. The Painter of the Wind
5. Pinocchio
6. You Who Came From the Stars
7. Guilty Akuma to Keiyakushita Onna
8. My Girl (kdrama, 2005)
9. Queen Seon Deok
10. Lie to Me
I'm more into sageuks and melos, but I won't say no to a good rom-com either

1. Empress Ki
2. Sorry, I love you (k-vers)
3. Scarlet Heart (c-vers)
4. Hana Yori Dango
5. Iljimae
6. Gu Family Book
7. Full House (k-vers)
8. Liar Game (j-vers)
9. Ja Myung Go
10. A Thousand Days' Promise
my all time favorite :
 
 1.signal : a master piece 
 2.the princess man
 3.cruel city
 4.school 2013
 5.W
 6.golden rainbow
 7.49 days
 8.D_Day
 9.healer
 10.six flying dragons
My top 10

1. Signal
2. It's Okay, that's love
3. The Princess' Man
4. Dong Yi
5. Moon Embraces The Sun
6.Goong
7. Empress Ki
8. Oh My Venus
9. I have a lover
10. Marriage, Not Dating


hehehehe
Here are mine in case you haven't seen them! ;)

1. It's Okay, That's Love
2. Signal
3. God's Gift -14 Days (it was amazing, but the last 30 minutes...)
4. King2Hearts
5. Liar Game
6. Kill Me, Heal Me
7. Remember
8. Love Shuffle
9. Beautiful Mind (it was cut though! ;A;)
10. Producers
It's hard to choose, but I think these are my top 10 dramas (in no particular order):
  • Ouroboros
  • Queen In Hyun's Man
  • Vampire Prosecutor
  • My Name is Kim Sam Soon
  • Legal High
  • Nodame Cantabile
  • BOSS
  • It Started With A Kiss
  • Goong (Princess Hours)
  • My Girl
I may change my mind the next time I think about this though...

(Check out my full list here.)
The Greatest Love
Splash Splash Love
Master's Sun
Love Sick
Falling for Innocence
My Name is Kim Sam Soon
Like Love
Addicted
Protect the Boss
High School--Love On!

Wow--it was hard narrowing it down to 10!