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.