for recent dramas, you can go on viikii.net
(you must have seen some videos from that site on mysoju.com)
It is great because you don't have to wait for long before starting to watch new drama, really quick work! And if english isn't your first language, you have the chance to maybe watch with other languages subtitles!
Jdramas and Kdramas that I have found good (with more or less romance in it, not all):
Japanese drama:
"attention please", "number one" and "Ace wo Nerae!" are three good jdramas with the same actress(Ueto Aya). the first is about flight attendants and their training, the second about a female volley team and the third about a tennis player.
Ganbatte Ikimasshoi
Nobuta wo produce (school drama)
dragon zakura (school drama)
Golden Bowl (about bowling, not bad)
Pride (it's about a hockey player)
Absolute boyfriend (rather funny love story, at least the beginning...)
kimi wa petto (funny drama)
Mei-chan no Shitsuji
Bloody monday
Life (dark side of high school in Japan, bulling)
first kiss
Untouchable (same actress than the famous "gakusen")
Kdramas:
City Hall
Fated to love you
why did you come to my house
What star did you come from
terroir
My girl
loving you
don't ask me about the past
summer scent
...
Drama currently airing that I'm watching:
"Obstetrics and Gynecology Doctors" Korean drama. If you aren't too bothered with blood it is really good! I cried with every episode though!
Stars falling from the sky
down with love (it's a taiwanese drama. funny)
That's what came to my mind. there is a lot but lots more that I must have forgot. I try to not put dramas already quote.
hope it helps!