The only opening scene that has left an impression on me is Adamas.
I never ff'ed through it. I liked it a lot more than the show itself.
It reminded me strongly of Catch Me If You Can and its beautiful opening animation.

Mr Queen has my favorite opening title. The paper collage effect is creative and I watched it every time...the music was a plus too!

It might not count but I liked the photo of the five friends they dropped throughout the beginning of every Hospital Playlist episode.

Love Between Fairy and Devil and The Nokdu Flower have opening sequences which I never skipped because I loved both the songs and the images.

I usually enjoy watching animated opening sequences, as in Meow (Secret Boy), Yumi's cells, Once upon a small town, Do do sol sol la la sol... And other times I like them also because of the opening song/music (The best hit, Weak Hero Class 1, Duty after school).

I have to mention another one that I liked despite its simplicity: Start-Up.

I am an opening credits watcher. But not to the point of enjoying the nuances in it. However, I did like the intro sequence in One Dollar Lawyer. It was something didn't necessarily look forward to but most definitely enjoyed cause I didn't skip a beat. The cartoon thingy was a spot-on good choice.

An intro sequence that is my favorite is actually that of a Chinese drama - The War Princess, Li Wei-young. For one thing, it featured it's main OST, If Heaven Has Compassion, which got to me the moment I heard it. And then the sequence provided an insight to what timeline we are in in the story.

And I really liked Go Back Couple's intro. It's silly. Especially with them shooting zaps of electricity from...is it thier hands or eyes.

Kingdom's opening is enthralling, it feels similar to The Crown's, but scarier. Haha...

I like When the Weather is Fine's, I think it sets the show's tone really nicely (but then again I like everything in that show so maybe it doesn't count!).

Crash Landing on You's split screen is very engaging as well, I watched it closely every episode to spot the differences between the two countries.

Alchemy of Souls' openings - it was fun to see the differences between seasons 1 and 2.

Oh yes I am!

Some of my faves include the ones from Romance is a Bonus Book, When the Weather is Fine, Chocolate, Love btw Fairy and Devil (Cdrama).

I remember when I posted the answer on @anne18 post and I thought "oh my god, it will be so hard to actually make a list".

Taxi Driver 2 : I love the music, it reminds the old US shows I watched when I was young like Knight Rider.

Little Women : It was beautiful and creepy in the same time. The colors looked intense.

Mr Sunshine : The ambiance and the song suited so well the drama.

Extraordinary Attorney Woo : It was super cute.

It's Okay to Not Be Okay : It suited the fairy tales theme.

The King's Affection : for the OST and the cute moving drawings.

I just want to give a shout out to The Secret Life of My Secretary and its super cute animation-esque opening title. The fact that the production team absolutely have fun with the "fish cult" even before fans (or beanies, really) started speculating on it just added extra fun on it.

Yes, I am.
They usually contain lots of clue and information for entire series (well, most of them 😉). I admired the one coming from Studio Dragon mostly (for sure they have a big budget tho 😅).
Recently, they have better opening credits, especially with significant OST. Many of them have memorable opening credit and worth to be mentioned (I mostly enthralled with anime/cartoonist/ miniature arts craft one):

It's Okay to Not Be Okay
Love between Fairy and Devil
While you Were Sleeping
The King's Affection
Business Proposal (on some level 😅)
Alchemy of Souls (on some level too)

Opening credits have gotten so good lately! Of course, can I think of specifics? Nooooo. But I’ve begun watching them every episode instead of my usual habit of watching for only the first and last episodes.
Right now I do love Bad Mom opening credits with the adorable piggy running through the scenes!

Great topic, opening title sequences are one of my favorite parts of kdramas! (and then it often goes downhill from there). Ever since Mad Men, I've been fascinated particularly by cool animations that set the mood, like the running sequence in Becoming a Billionaire. Awaken has an inventive and creepy opening using miniatures. Possibly my favorite is My Ajhusshi which filters live action in painterly effects (probably not the the correct term, but we used that when I worked in computer graphics). Cinderella's Sister did the same thing.

I remember the animated title sequence for 'Sh**ting Stars' left no doubt why the translated title got two asterisks instead of spelling the word out.

Favorite:
Crash Landing On You: I love the way they pass by each other; it contains hints for how the leads were connected.

To be honest, I usually skip over this part.

Memorable opening sequences:
Kingdom
Mr. Sunshine
It's Okay To Not Be Okay
Alchemy of Souls
All of Us Are Dead
Little Women
Lost

i love the (i call) retro graphics opening sequences -- reminds me of the 60s hollywood movie era, especially the Pink Panther series. Jdramas had been using cute animations or cutout images that i have seen replicated in Kdramas... i love the art!!!

i notice all the "hints" in the openings, but there are usually too many to figure out, so as the story progesses, these hints make more and more sense without spoiling the story. kudos to the art directors!

My favorite opening title is Love All Play's because its "When The Door Opens" OST is my ultimate mood booster and its adorable animated sequence turns the shuttlecock into a heart.

From recent memory, 'Call it Love' was brilliant. I loved the play of shadows and each frame was beautiful.

Others that I really loved
Adamas - Great intro of the main character- The house! and beautiful play of shadows.
Happiness - Wow!! It was just WOW! That music still haunts me.
Kingdom - Hauntingly beautiful!
Hyena- I really like how the contrast of both the characters were shown through objects.

Has it been said already? Don't know, will check in a moment, but always and forever KINGDOM!

Kdrama ones are usually short so I don't typically skip them. They're also a newer phenomenan in my experience.
Some of them really set the scene for the drama (Kingdom, Adamas, Call it Love as a few examples) and add to the experience and as others have said, have clues or thematic significance. Some are just fun, cute or clever in style. Some are unnecessary. Some I could do a better job for and honestly, I think about how I'd make opening sequences for my (unmade) TV shows all the time.

Cdramas I usually watch for the first few EPs, then skip, then I always like to watch start and end credits fully for the last episode lol. (I've always been a movie credits watcher, long before Marvel made that mainstream 🙄). They're usually longer though so it's also good for getting ready before watching, you can start and still have time to settle in.
Also sometimes if the song is extra good or the art extra beautiful (LBFAD) you don't want to skip. I am not sure I skipped a single opening of When We Were Young 2018.

Kingdom is my go to example though, and still probably my favourite after all this time. It's a genuine traditional funeral rite preparation, it's shot so beautifully and chillingly and it is PERFECT for the show. I adore it. It's probably actually my favourite part of the franchise now 🤣😅.

I guess I'll be the first to say it....I almost always skip the opening and ending sequences. Most of the time I find them annoying because they're between me and the next episode lol. Cdramas have made me better appreciate the shortness of Kdrama intros though...I usually only have to hit the skip button 3-4 times to get through a Kdrama intro, where Cdramas take 10-12 skips usually.

However, I will say that a couple of Cdrama OST's have made me pause a handful of times to watch the intro - Love Between Fairy and Devil, Who Rules the World, and now Love Like the Galaxy. I guess I'm drawn to the more cinematic style openings.

I can actually remember if it was played more over opening or ending, I think ending? but Jannabi's Variegated for EX GIRLFRIEND CLUB was fantastically perfect as a theme and ending song, and honestly elevated and made the show that much more fun. I never skipped it haha. It was also the song that got me into Jannabi, and one of the first Korean songs I learnt the lyrics for ever.
But that's kind of a "credits" song or theme song and not specifically about the sequence itself, because I don't think their really was a sequence, it was mostly just freeze frames of however the episode ended, and the song fading in on whatever toribke the characters had got themselves into now. I guess that does count actually. I can't properly remember though, it's been a while re. the show. Still listen to the song though 🤭

The one that stuck with me the most was Innocent Man. It would play about a minute or two into the episode. The combination of the music, song joongki frowning and his one tear, and the pocketwatch ticking backwards. THE ANGST OF IT ALL! And then during the last episode, time moves forward again and he's smiling (with tear falling)!

I do enjoy how more opening title sequences are animations. They're just so cute!

As an older U.S. t.v. fan, I have vivid memories of the junk t.v. I watched starting in the late 1960s-1980, and the openings of ALL of them stick in my mind, and their songs immediately trigger memories. I could probably hum the theme songs and visualize the openings of of all them, from Wide World of Sports, Wild Kingdom, Mission Impossible, Hawaii-50, through the Brady Bunch, Wonder Woman, the Six Million Dollar Man, etc. etc.

Given this, I really like kdrama openings, and never skip them, because they often become what I think of when I think of the show--so if the show is decent, I remember the opening favorably. Its Okay, Her Private Life, Hometown Cha Cha, etc. Recently, I really liked Taxi Driver for its brief but rockish beginning My current fave is Bora--its also short, with striking graphics and memorable-catchy music. Like @spazmo I'm also a big fan of jdrama openings. The cutouts are really artistic, again combining beautiful graphics with good theme music.

Nothing against Cdrama openings, but because of the lousy translations of the opening songs, my wife and I have found it hilarious to try to sing the translations along to the music. No fault of the openings themselves or the songs, of course--its just the translations. So I just can't take them with the same amount of seriousness I take the Wonder Woman theme.