Rich Guy Falls for Poor women or Vice versa

Shopping King Louie: Rich male lead, poor female lead. A really uplifting cute, fluffy drama where the guy does fall for the girl first. Would say this one is the first to spring to mind with the rich/poor trope and there's a whole lot of adorableness between the leads.

Healer: Male lead is rich but also a loner (kinda cold-seeming at first but actually sweet), female lead is not poor but from a humble upbringing. Both of them are strong-willed in their own ways. As far as I remember, both of them start to fall for each other around about the same time? The romance is also very sweet with cute moments.

Strong Woman Do Bong Soon: Male lead is a rich CEO, female lead has super strength and is from a humble background but can kick ass. The pairing plays out like a reverse bodyguard trope (the girl is the one protecting the guy) and there's a lot of teasing between the two.

The Master's Sun: Male lead is a rich CEO, female lead sees ghosts. Can't comment much as I haven't watched this myself, but I've been recommended it.

Rooftop Prince: Male lead is a Joseon-era prince who gets transported to modern day, female lead is relatively poor and living in modern day. Definitely recommend for the comedy elements (it's rare that a drama makes me laugh that much), and the romance is slow-burn that starts out as a love-hate but sweet with plenty of bickering/teasing.

Suspicious Partner: This doesn't really fall into a notable enough rich/poor category, but the male lead is higher status than the female lead, and is more financially well-off. Male lead seems cold/harsh at first but is really caring and is kinda a tsundere type, female lead is a former national Tae Kwon Do athlete and more than capable of kicking ass. There's a whole lot of funny/sweet moments with plenty of teasing and bickering too.

Maybe Bride of the century or Mask (2015)

• 1% of Something - the ML is rich, rude, and a tyrannical boss. The FL is a teacher. They strongly dislike each other in the beginning, but once they are forced together the ML quickly falls for the FL and begins to soften up / show his softer side. 
• General and I (I'm still watching this one) - ML is a successful general / prince who faces off in a battle of wits against the FL, who is a military strategist / maidservant to the prince of a rival state. They are enemies, and the female lead in particular literally tries to kill him at one point, but they actually have a childhood connection and the ML has liked her / been grateful to her since they were kids. She takes a bit of time to warm up to him. It's a long drama, but it has a lot of what you're looking for.
• Sassy Go Go - the ML and FL are leaders of rival clubs. The FL is the leader of a dance club for the students with the worst grades in school (poor), while the ML is the leader of a club that is really just a study hall for the students with the top grades in school (rich). 
• Weightlifting Fairy Kim Bok Joo - this drama is set in university where the leads are both athletes. The ML is a handsome and popular swimmer (his family is well off but not mega rich). The FL is a weightlifter (her dad runs a chicken shop), and although her teammates are good friends to her, they are looked down upon by the more feminine girls on the gymnastics team. The leads don't "hate" each other, but they don't start out on the best foot. When the ML realizes she's the girl he had a crush on when he was little, their relationship turns into one where he teases her. Eventually they become very supportive and sweet. Lots of cute moments. 
• Boss & Me (I didn't finish this one) - the cold, rich boss of a large company falls for a poor entry-level working girl. Very fluffy.
• I Need Romance 3 - the FL looked after the ML when they were kids and he developed a crush on her before moving abroad, where he becomes a successful song writer. The FL grows up to be a cold team leader for a home shopping channel. When the ML first meets her again he immediately dislikes her new personality, but decides to figure out why she changed after learning her identity. When the ML reveals his identity to the FL, she rejects him because she hated taking care of him when he was a kid and only sees him as an annoying younger brother that she was forced to take care of. So not exactly a "hate" relationship, but definitely a rough start. The ML is extremely adorable and they have lots of cute moments. 
• Sound of the Desert - the male leads are the head of a very wealthy merchant family and a successful general. The FL is penniless in the beginning (living in the desert with wolves) and she is both strong willed and physically strong. The merchant guy is sometimes a bit cold, her relationship with the general involves a lot of teasing, and the love triangle creates some tense moments. There are also a ton of cute / sweet moments. 
• The Eternal Love - the ML is a prince. The FL is a real estate agent. It might not be outright "hate", but their relationship starts off badly - they are in an arranged marriage and the FL is constantly trying to escape while the ML suspects her of spying on him for his brother and rival. There is teasing and some very cute / sweet moments. 
• She Was Pretty - the ML developed a crush on the FL when they were kids before he moved abroad. The female lead goes from beautiful to "ugly" as they get older, and when the ML returns (now wealthy and successful) she is embarrassed to meet him and asks her good-looking friend / roommate to go in her place. Of course the ML turns out to be her new boss. Craziness ensues. Their relationship is sort of love / hate for part of the drama (he's mean to her partly because he feels she's not good enough to have the same name as the girl he has long had a crush on, and partly because he feels guilty for slowly falling for her), and later on there are cute moments. 
• W Two Worlds - the ML is an olympic gold medal winner / rich CEO of a company / TV show that catches bad guys from difficult cases (and a manhwa character). The FL is a doctor with a mean teacher who lives with her mother and is the daughter of a manhwa artist. The ML is somewhat suspicious of her, and although he protects her from the police he also refuses to let her go until she explains certain things to her, so he sort of has her under house arrest. He's charming and persistent in the beginning, but once he commits to the idea of romance, he also shows his cute / sweet side. There are lots of sweet moments and some cute teasing.