I second autumn iris' recommendations of Falling into You and The Love You Give Me.
High school romance: When I Fly Towards You
College romance: Hidden Love
Noona romance: Falling into You (I always enjoy Wang An Yu)
Working romance: Moonlight
Romance with comedy: Filter
For romance with a touch of drama: Road Home, You Are My Hero, Fireworks of My Heart
Second chance romance: The Love You Give Me
Romance with the best OST: The Day of Becoming You
Honorable Mention romances (not my favorites, but I have an impaired sense of romance; other people like them, and I found things other than romance to like about them): Hi Venus, As Beautiful as You, Sunshine of My Life