I'm looking for a drama where the male lead betrays the female lead and it's a semi/very important part of the drama and she doesn't forgive him easily or maybe doesn't at all. It can be historical or modern and from any country. Some examples I can think of are Goodbye My Princess, Familiar Wife (it's not so much a betrayal and she doesn't have to forgive him, but the dynamic with a ML who is trying to right a wrong is similar here), New Tales of Gisaeng, Royal Nirvana, Ten Miles of Peach Blossoms, and My Girl. 

You can try The Promise (Kdrama version)

 looktothestars:
a drama where the male lead betrays the female lead and it's a semi/very important part of the drama and she doesn't forgive him easily or maybe doesn't at all. It can be historical or modern and from any country
  • The Legends - The ML's betrayal is major, but not intentional.
  • Why Her? - The ML hides his identity from the FL and it's a big deal.
  • Zhang Gong Zhu Zai Shang - The ML hides his purpose / mission from the FL and it's a big deal.
  • Misty - My memory is a bit fuzzy so please forgive me if these details aren't 100% accurate. The ML is involved in murdering his wife's ex. His wife becomes the prime suspect for the murder. The ML takes on her defence (he's a lawyer) and pretends to be on her side when he's really using the situation to get closer to her while basically making her take the fall for his crime.
  • Tempted - The ML woos the FL into dating him based on a bet / game with his friends rather than genuine feelings.
  • Moon Lovers: Scarlet Heart Ryeo - Instead of marrying the FL, the ML chooses to marry someone else who can help solidify his power. That choice is the final straw for the FL and she chooses to marry the ML's brother in order to leave the ML / to escape the palace.

Ooooo thank you both! I've seen The Legends and Moon Lovers and loved them both. I'll definitely try the others!

V.I.P. cheating is involved.

 Rien:

V.I.P. cheating is involved.

I love Jang Nara, I'll definitely give it a watch. Thank you!

 Saygo :

Omg yes The Wolf hurt so good lmao. The other two are high on my to-watch list. Thanks!

Bloody Romance - not a cold betrayal but  at  important moment he doesn't prioritize her and she gets hurt because of it. It does have consequences.

 Marpleme:

Bloody Romance - not a cold betrayal but  at  important moment he doesn't prioritize her and she gets hurt because of it. It does have consequences.

I've seen Bloody Romance and I really liked it. That moment stung in the drama!