Startling By Each Step (步步惊心) - It's one of the best historical dramas I've ever watched (and it's also one of the best time travel dramas out there)! It's chinese, but even if you're not into chinese dramas, it's totally worth it. : ) It's gorgeously filmed and the soundtrack is perfect. It's really intense and addictive, but at the same time there's a lot of heart-warming and funny moments. You'll have to give it about 5-7 episodes before it becomes really good, but after that you'll be hooked!
It's about a girl that travels back in time after an accident. She wakes up in the body of her old reincarnation Ruo Xi and starts working in the palace. There she befriends the princes of the throne and it soon becomes complicated (because she knows their fate and what'll happen to each one of them). She does everything in her power to not affect the course of history, but it's not always easy to make the right decision when you're already in to deep.
Genre: Historical, Time Travel, Romance, Friendship, Drama, Comedy.
Hong Gil Dong (쾌도 홍길동) - Even though I really recommend you to watch Startling By Each Step, I might as well recommend some other dramas too. Hong Gil Dong is a korean drama and of what I remember it was really fun to watch and I liked the main couple, it's not the best drama out there, but it's still really good. Oh and Jang Geun Suk plays one of the four main characters, haha!
It's based on a book about Hong Gil Dong, the korean version of Robin Hood. He fights injustice in the corrupted society togheter with his friends. One day he meets Heo Yi Nok (the dramas heroine) and Lee Chang Hwi (the rightful heir to the throne) and the real adventure begins.
Genre: Historical, Action, Comedy, Romance, Drama.
Tamna, The Island (탐나는 도다): Also called Tempted Again or Tamra, The Island. This drama is absolutely gorgeous. It's sweet, funny and you'll come to love the main couple! In the beginning it's just so-so and you might think that it's a little bit silly, but after only a few episodes it will become really good and addictive. I really recommend this drama!
I don't know how to explain the plot more than this. It's set in 17th-century Joseon dynasty and there's a young english castaway named William who comes to an island called "Tamna" (todays Jeju Island). There he meets the clumbsy village girl Jang Beo Jin and they become friends. At the same time there's another man coming to the Island named Park Kyu. He's under disguise of one of the many convicts sent to the island (not going to tell you his real identity even though many wiki pages do) and even though he doesn't really like Jang Beo Jin he's forced to live at their house during the stay.
Genre: Comedy, Historical, Romance, Adventure.