@DreamingKoreanBallad Death Note Ghost-Seeing Detective Cheo Yong Line Romance
@LaughingCheshire Who Are You!!!!
@jumpstar City Hunter!!!! best drama I've ever seen :)
@HeroGirl Buzzer Beat Coffee Prince
@Gajin_ Ataru Risou no Musuko
Hi MusicROSE, I recommend Boku no ita jikan -- it is sad, but also really, really sweet. Or Tempest, if you feel more like historical with a touch of fantasy.
Nobuta Wo Produce My Boss, My Hero Buzzer Beat Kurosagi
I'll recommend you God's Gift - 14 Days and for a movie The Man From Nowhere (but is violent, if you can't then don't watch it)
Cruel City, Vampire Prosecutor and City Hunter.
@Cheer

a man's story!
Bloody Monday
Rurouni Kenshin

those three are all my favorites
@prettytin: Adolescence Medley,King2Hearts,Rooftop Prince. My favs among yours :)
@Rhopalocer  

Watch "Miss Granny" and a "Werewolf boy"  and then for dramas I would say "Discovery of Romance" and "Night Watchman's Journal".

A nice mixture of a little romance and a little spooky. 
@Sterl-z

I Need Romance 2 has the same female lead as Discovery of Romance and I highly recommend it. Then maybe I Need Romance 3 afterward.

Also, Nine: Nine Times Time Travel is one I'm watching and loving right now.
@Lyn: There are many on your list that I really like, but for romance dramas I'd narrow it down to Dal Ja's Spring, Protect the Boss and Queen Inhyun's Man.
Sungkyunkwan Scandal is a good introduction to historical dramas and Golden Empire is an awesome business drama, but be aware that it's purely focused on the business aspect^^
@risingsun: I like to recommend a few J-dramas from your ptw :)

Soredemo, Ikite Yuku
Hanzawa Naoki
Orange Days
Tonbi