Hyena
A drama that pretty much fires on all cylinders from the word "Go", the writing, the perfomances, the worldbuilding are pretty much aces from the first episode.

World of the Married
An artistic, highbrow take on the makjang drama that does an excellent job at setting up the trashy rollercoaster that will follow for the following 15 episodes, its also far superior to its british original imo ( Surrane Jones was absolutely fantastic in the original though)

The most recent ones that I can recall having great first episode are:
Extraordinary Attorney Woo
Taxi Driver 2

What a fun prompt! I can't wait to read everyone's answers. A short list of what I would consider great first episodes to great dramas includes:
Like Flowers in Sand
The Matchmakers
Bossam: Steal the Fate
Mr. Queen
Healer
I would also add, for my personal preferences of greatness/first episodes, Unlock My Boss and Into the Ring. While I wouldn't say I loved the whole drama, While You Were Sleeping has an EXCELLENT first episode, too.

Money Flower

The list is endless but...

Trolley
Queenmaker
Why Her?
Our Blues - I pressed play on this solely because of the first 3 episodes.
Uncle Samsik - You have to watch this to know this.
Queen For Seven Days: This one is beyond the first episode. The introductory minutes alone is something else.
Arthdal Chronicles 1.
Tell Me That You Love Me.
The World of the Married.
Cheat on Me If You Can.
Behind Every Star: Jo Yeo-jung and Seo Hyun-woo sold this drama to me with their bickering chemistry in episode 1. The people who matched that bickering chemistry again in the show was Park Ho-san and Oh Na-ra.
Adamas.

Perfect Marriage Revenge it was prefect from the get-go. 🤣🤣🤣

Episode 1 wasted no time, set up all characters, we knew what we could expect and wowza 😱 did it deliver. 🙌

Mr. Sunshine
Young Eugene (Kim Kang-hoon’s) performance was just amazing.

Happiness
I blindly jumped into this without watching any teasers and all I can say is the lead’s instant chemistry is probably one of the best I’ve seen in the last few years.

I haven’t watched all of it, and I’ll definitely get back to it at some point but the first episode of MY LIBERATION NOTES is incredible.

I’ll also add ATYPICAL FAMILY as well, it’s pilot episode is confusing and yet unique and intriguing, pretty much as the title suggests ATYPICAL

*And just a note: don’t get caught up in thinking about great dramas with crappy first episodes yet — we’ll be chatting about that next time.

LOL
And we need crappy dramas with great first episodes as well 😂

The opening of HAPPINESS is both bonkers and immediately establishes the OTP's respective characters. Can't ask for more than that from a first episode.

I also loved the first episode of ROOKIE HISTORIAN GOO HYE-RYEUNG with the OTP's hilarious meet-cute in the bookshop and where we get a very clear picture of how awesome the FL is.

Healer.

This is a gimme, but I'll take it. That first training scene in the hideout (video game tennis, of all things)...straight into the subway/train spy action with Ajumma.

I was there from the first seconds.

I remember Alchemy of Souls having a really fun first episode. It has a lot of history to establish right off the bat but doesn't falter as it moves into the present, and then the introduction of our two leads was just glorious. We know who Jang Uk is immediately, and Naksu/Mu-deok is at her most murderous. We get amazing interactions with Uk being held at crab-leg-point and telling Mu-deok she has beautiful (soul-shifty) eyes. His request at the end that she be his master is an incredible intro to the rest of the whole story. Makes me want to rewatch right away!

Kingdom - they had my complete attention right from the title opening credits. It really was a terrific opening right from ep 1.

This is very interesting. Because with many of my favorite shows I skip the first episode on rewatches.

A Korean Odyssey. That might be partly because I grew up watching Monkey, so I was giggling at a contemporary Monkey, Pigsy, and Sandy even without any story. (Bull Demon King was an extra character, but done so well he had me giggling too)

So many :
- Goblin : I need Gong Yoo in a sageuk!
- A Piece of Your Mind : I loved the atmosphere of this drama.
- Extraordinary You : the world of manhwa with Danoh discovering she's not the FL.
- Heartless City : just for Jung Kyung-ho knife fight.
- Start-Up : Nam Da-reum was too good as the SML's backstory. It ruined the whole drama.
- Castaway Diva : these teenagers were very good, I could have watched a whole drama with them.
- The Matchmakers : It was so beautiful and funny.

The first episode of While You Were Sleeping is a self-contained movie.

Getting back to my list, I was surprised that there are countable ones that fit the bill.
Under The Queen's Umbrella
Bloody Heart
Extraordinary Attorney Woo
Tomorrow
Our Blues
Me Sunshine
Twenty Five Twenty One minus the ending
Call it love minus the time jump
My Dearest 1
Doctor Cha
Flex X Cop
Me Queen
Kairos
Defendant (I am 4 episodes in but I added it to my favorites)
Little Women

Under the Queen's Umbrella. I was sold from the first minute!

It is a very big call for a great first episode - which normally comes around episodes 2 - 4.

Since no one has mentioned it, I’d say One More Happy Ending hit that rare note of getting you in the first 60 minutes. I was so enthralled by that very first episode as we saw the opposite-attract meet of Jung Kyung-ho and Jang Nara, getting drunk together to marriage registration - all within 24 hours. So charming and funny! I was thinking what an amazing first episode and looking forward to a nice romcom….but no.

I would rewatch it every now and then - but only the first episode to re-live that great promise.

D-Day had a pretty unforgettable opening episode. And I thought Flex x Cop did a great job setting up the characterizations in it’s first episode.

I don't have a good memory for details, but I still remember how I was impressed by the cinematography and how one scene morphed into another in It Is OK to Not Be OK.

Interestingly, most kdramas truly take off in Ep2-3, not the very first one. Esp older shows where those initial episodes were all about setup/flashbacks. Take LOVELY RUNNER for example - it's not like Ep1 was objectively weak or anything, but people really got invested after the twist in Ep2. Plus sooo many sageuks that are better with their prequels than actual story - GU FAMILY BOOK, MOON EMBRACING THE SUN... legion of them!

Since people already mentioned HAPPINESS, I'd go with FLOWER OF EVIL, that opening episode was fire (look, PD who knows how to do tension and cliffhangers!). Now that we're talking about it, BEYOND EVIL (precisely Ep1 ending) was quite good too. Right, THE CROWNED CLOWN! All the titles we already mentioned these days))) REVENANT too. I also loved THE FIERY PRIEST's one but I'm probably in minority here... Right, k-SUITS! Another PD with a solid vision. ARANG AND THE MAGISTRATE as well.

For cdramas - TILL THE END OF THE MOON says hello, that intro alone should be in fantasy genre textbooks. Also counts for the most epic introduction scene of ML - twice in the same episode, 3 times in the whole show because tiny LYX can outrizz a crowd without breaking a sweat^^

Yumi's cells would be one of them, no doubt. Amazing drama with an almost perfect script.

Other dramas with a great first episode which kept being very good until the end:

_ Prison Playbook. Wonderful from the first minutes.
_ At a distance, spring is green.
_ Twinkling Watermelon.
_ Live up to your name.
_ The Nokdu Flower (such a powerful and hard start).
_ My Dearest. (But the best episode was the sixth).
_ The Atypical Family (this drama got better from the fourth episode, though).
_ Weak Hero Class 1.
_ My Ahjussi (currently watching it for the first time. 7 out of 16 so far. But my favorite episode has been the first one).

One of the best first episodes I have ever watched is from Start-up, but even though I really like that drama, I think the first episodes were above the rest.

I just rewatched Yumi's cells and it really was that good, just as I remembered. The other standout first episodes for me were The Producers, Racket boys, Hospital Playlist and Reply 1988.