Hotel del Luna also deals with this in a big way. Man Wol is not reincarnated, just super ancient, but pretty much all the other major players in her life are. I love the idea that your connections to people linger through lives, but they might take very different forms from one life to the next. Also, the fantasticness of IU's wardrobe in this drama is not to be underestimated.

Tomorrow is another drama that I enjoyed that dealt with reincarnation (pretty much whenever death is a big topic, I think reincarnation follows). It wasn't quite as big of a thing in this one, but in one of the episodes you find out what the male lead was doing in one of his past lives (being generally heroic) and it's important to one of the people that the team is trying to help.

I know that this was one of the options on the Beanie Awards, but I think that Bulgasal also did this really well. I really loved this drama in all its moodiness. I loved that they revealed the story of the characters' past lives little by little (as the characters themselves remembered/figured them out) and that we didn't have a complete picture of what really happened all those centuries ago until the last episode. Plus, Lee Joon is so magnetic in this role, and Lee Jin-wook is one of the best brooders I've ever seen.

You Who Came From the Stars : The ML met the first time the FL in the past, when he met her in present area.

Rooftop Prince : The ML time traveled in the present and meet the FL who is the reincarnation of his sister-in-law.

Tale of the Nine Tailed with the FL

Extraordinary You : it's a little bit different but it's kinda the same principle :p

From Now On, Showtime! Such a beautiful story about a lost love and how it impacted all of the characters' destinies. I was as invested in the past romance as I was in the current day one.

Bulgasal and Go Back Couple

Chicago Typewriter, classic example of a reincarnation story - memories of the past life informing the present in interesting ways. Also interesting to note how the good and bad people change or stay the same in the second life.

Also in case you chance upon it while looking up reincarnation dramas, do not watch Born Again. No matter how tempted you are by the fact that it has Yang Se-jong and Lee Soo-hyuk, don't do it!

I’m gonna take the definition of reincarnation literally (a person or animal in whom a particular soul is believed to have been reborn)
And say Zombie Detective :P
Also any Vampire Kdrama I guess, but I haven’t watched any of those…

I like fantasy dramas and so had decided a while ago that it's a common trope that something tragic happens in the distant past, and the drama concerns a repeat of the same pattern, with the protagonists managing to avert disaster this time. Commenters have already mentioned My Love From the Stars, Hotel del Luna, Extraordinary You, and Showtime Begins. I'd add Legend Of The Blue Sea, My Girlfriend is a Gumiho (though the reincarnation aspect is missing here), and Magic Pop-up Bar.

I've often wondered what this trope says about Korean culture and attitudes to history. Do they see the modern world as a kind of do-over for a tragic history?

The Abyss. Even if only for the scene with Jung So Min and Seo In Guk as know-it-all aliens explaining the premise to Ahn Hyo-Seop.

I actually had fun with this one, I know a lot of people didn't like it but that is often the case with shows I enjoy anyway.

Arang and the Magistrate has various forms of reincarnation, mostly not of the finding your lost love variety, but there's a soulmate thing going on at the end.

Chicago Typewriter is my favourite among reincarnation dramas. Both timelines were good and I really like how the remembrance of the past shine through in the present as the show progresses.

Han Kang Bae and Kang Yeorin, even Chief Gwi in Mystic Popup Bar are total reincarnation story that destined to met...

It would be terrible to have been a really good person in one life and have a karmic stuff up after death resulting in reincarnation as an annoying and screaming windbag/horrid school bully/toxic relative. And, then remember who you used to be. What a nightmare. It is good that it is all implausible (I hope!).

Extraordinary You is probably the only one of the reincarnation dramas that I really enjoyed. I liked it so much that I started visiting the trumpet vines in a beautiful garden near my house. (The flower that was the symbol of the reincarnation plot was the trumpet flower.) I was surprised when I found the manwha scanlation online that the trumpet vine was apparently an addition by the drama writers. Everything about the way the reincarnation plot played out was so delicate and clear, not confusing like those plots sometimes are.