My wife is the real Kdrama nut, I think she's on her way to the point where she's literally watched everything. I'm more picky and join her when something catches my interest. And it's turned out to be a Netflix original nearly every time, so I am, through no fault of my own, a corporate shill.
Cheesy romance wise, I probably best liked Crash Landing on You. First of all the sheer production value pulling off the concept, and second of all the drama doesn't spend its entire run in the comfort zone of "will they? won't they? can they? can't they?" that 90% of dramas seem to wander around endlessly up to episode 15.9. At some point the ML and FL just... get together and do couple stuff while the crazy plot goes on around them, I say that's a seriously underrated feature. The show's weak point was the villain who at every point was exactly as menacing and resourceful as he needed to be: one moment he can teleport anywhere, follow anyone and summon infinite henchmen, the other moment he fumbles all his advantages and comes inches from death. It's clear the action and intrigue weren't the main focus for this show, and were used more as enablers for the star-crossed lovers to act out their story. Also I will never get over how the filming for this show involved two actors who were totally into each other and trying to hide it, playing two characters who were totally into each other and trying to hide it. I can just imagine the crew sitting there and thinking "wow! This is really believable acting!"
Intrigue wise -- I'm tempted to say "Defendant" just because of the insane opening theme and the ML's memetic rage ("CHA MIN-HOOOO!!!!!!") but the one that comes to mind is the recently-released "The Glory". It is basically a sprawling and visceral revenge plot; a bunch of assholes being set up to destroy one another by the person who they wronged, where the lead asshole puts up a fight and you always have this suspense of "who thought X+1 steps ahead this episode". In that respect it's similar to the non-Korean Revenge (2015) starring Emily VanCamp (but thankfully avoids that show's profound seasonal rot, which culminated in a final season built on the premise that the one character whose death set the entire show in motion was actually alive after all -- I feel no shame in spoiling that). A similar and even grittier experience is "My Name", also a brutal revenge story that invites you to guess the twist between one gut punch and the next.
WTF-wise I recently watched "The Interest of Love" and could not look away from it, like a terrible car accident. I don't even know what to call it, the negative inverse of a love story maybe. When I grow old and forget every other kdrama I will still remember the FL from "The Interest of Love" and her pithy, soul-destroying one-liners. At some points I remember clapping and cheering at the particularly cruel ones as a defense mechanism. I don't have the words to articulate the gaping hole at the core of this drama where a heart should be; maybe I can say the big emotional idea is kind of like the Basic Instinct movies -- deep down the ML knows he is being slowly eaten alive but he won't walk away, he can't walk away, deep down in a perverse way he wants this and needs this, and so do the writers, the lord have mercy on their souls. It was certainly an experience, a piece of impossibly sour candy.
Sci-Fi wise I fondly remember "Sisyphus". It's the mirror image of "Crash Landing": The love story is nothing to write home about, but the surrounding plot, wew lad. There's time travel and an evil future at war with the present, basically like a more intelligible version of Nolan's TENET. I can barely remember any of it now but at the time I remember being decently impressed with it, and that's after reaching a point where I felt I've already seen every kind of sci-fi bullshit and nothing could impress me anymore. I particularly liked how they skirted around the whole issue of "how do the people with time travel not just stomp over all the obstacles in their path", which to my taste was disastrously handled in e.g. "Signal".