The Princess Wei Young - the FL's kingdom was taken over and her whole family was killed, and for a while the FL believes the ML's grandfather was responsible.
Crash Landing on You - The FL is from South Korea. The ML is a captain in the North Korean army.
The Princess's Man - The ML falls in love with the FL thinking she is someone else. There is a political conflict (a coup but I don't remember the details) and the ML is on a different side than the FL's father. The ML is exiled and the FL's father is responsible for trying to kill him. The ML becomes a rebel bent on revenge against the FL's father.
Love through multiple lifetimes or across time (time travel / different timelines / resurrection / reincarnation), often despite lost memories or a change in appearance:
General and I - epic love story through war. ML and FL have unwavering trust and love in each other. Both of them are very smart leads, they like challenging each other's intelligence lol. Lots of chemistry and skinship.