A third party forces them to marry. They don't like each other at first, but the male lead starts to fall for her. She likes someone else, but begins to fall for the male lead. By that point though, the male lead finds out about the other guy and doesn't trust her so she had to earn that trust back.

Siyah Beyaz Ask (Black and White Love) -  This is a Turkish drama and it has one of the best romances  I have ever seen! Highly recommended. The male lead is a sort of hitman who works for his uncle. He captures a doctor (female lead) and forces her to operate on someone. She overhears something she shouldn't have so the uncle orders the male lead to kill the doctor. He refuses to do so and marries her instead to protect her and to use her to protect his family from her brother who is a policeman.  

Goong - Princess Hours - girl get married to a a prince beacause her grandfather made a promise

Princess Hours - Thai version of Goong

Something about 1 Percent - a rich grandfather blackmails his grandson in order to make him marry a kind girl (it is more forced courting / dating)

The Crown Princess - An elite soldier need to marry a crown princess to cover her identity and protect her 

Leh Ratree - A father (kind of) sold off his daughter to a rich family to clear his debts - the son of the family doesn't want this arrangement as well as the girl

Eternal Love: FL is still fixated on someone else when her marriage with the ML is arranged. When they meet, they do not know each other's true identity and fall in love.

The Eternal Love: The FL possesses the body of a girl whose marriage has been arranged with a prince (ML). The girl was romantically involved with one of his brother's, but the FL falls in love with the ML.