Here's some Asian flicks you might want to check out :

Failan Sang-hoon Ahn 
Christmas in August Hur Jin-Ho
Sassy Girl Gwak Jae-Young
Love Wind-Love Song Park Dae-Young
If the Sun Rises in the West Eun Lee (not great, but fun)
Bus Stop Lee Mi-Yeon
Asako in Ruby Shoes Jae-Young (weird love story)
Camel Park Ki-Yong (man and woman cheating, rather 
       unique flick)
Oasis Lee Chang Dong
Sennen-Tabito Jinsei Tsuji (masterpiece)
Laundry Junichi Mori (fun and different love story)
Il Mare Hyun-Seung Lee
One Fine Spring Day Hur Ji Ho
Marriage is a crazy thing Yoo Ho (different love story)
Twilight Samurai Joji Yamada (not romance, but a 
         deep love story, along the lines of The Road Home)
Suzhou Ye Lou (different sort of love story)
Dolls Takeshi Kitao (not romance, different love story)
