Dramas like heartstrings where the lead girl falls for the lead guy but he is in love with another girl but eventually he falls for her. The girl can be lead or secondary. 

Warm and cozy
Gu family book 
Full House
Best Lover
Bring It On, Ghost
Cinderella and the Four Knights
Delightful Girl, Choon Hyang
Fated to Love You
Goodbye Mr. Black
Goong

Most of the recommendations I have watched but I see a few new ones thank you!!! 
Leh Ratree - Second lead fall in love with the (ex-)boyfriend of the female lead. (Love this two)
Gu Family Book - she is the only one who believes in him but he cannot get over his first love. She knows that but still wants to stay by his side

Do you also want recommendations where the female lead is in love with another person?
@real_mokona send me all the recommendations you have, I'm desperate. Hahahh 
ok... Dramas the female character is in love with someone else:

Dream High - she is in love with one but another guy is always by her side, protect her and doesn't expect anything
Boys over Flowers - She is in love with the best friend of the guy who has a hit on her
Thumping Spike 2 -she is interested in a volleyball Player and a popular guy helps her do get his Attention... but step by step he starts to really like her
Best Time - she start to work in a company to get close to her high school crush and meet a guy who is interested in her and can simply read her mind
Jealousy Incarnate - she is obsessed with one guy but when she fall in love with his best friend (after he rejected her) he starts to become interested in her and fall in love... but will he fight for her and stab back his best friend?
When a Man loves - a man falls in love with a Girl he saved once but she is in love with his friend... or does she just use both of them?
@real_mokona thanks!!! Best Time is the only one I have not watch. I will go look it up now.
Also wanna recommend:
Fight My Way
Scholar Who walks at night
lee soonshin is the best
rooftop prince
My GF is a gumiho
my Girl

Non-korean dramas:
Loving never forgetting
across the ocean to see you
Drunken to Love You
Sunny Happiness
H2
please love the useless me
kleun cheewit
More recommendations:

My lucky star
Nagareboshi
Wedding
Cain and Abel (kdrama)


Where the female lead loves someone else first:

That Fool
Pride
Weightlifting fairy Kim Bok Joo
Hotaru no Hikari
I'm Sorry, I Love You
It's Not That I Can't Marry, But I Don't Want To
Thanks @Izzydramalover
Wild Romance
Attic Cat
Innocent Man
The Incarnation of Money
My Girlfriend is a Gumiho
Goong
fated  to Love You cdrama
My Lovely Sam Soon
My Precious You
Dragon Zakura(it's not the main story )
Which Star Are You From