Here are few of the dramas that have become popular recently:
Goblin : A fantasy-romance drama about a deity who has been alive for 900-something years, looking for his bride, who can lift the curse of immortality from him.
Signal:
(No Romance) A supernatural thriller drama about a profiler who one day finds a walkie talkie, which helps him connect to a detective from the past. Together they work on solving many cold cases.
Weightlifting Fairy Kim Bok Joo : A drama about a girl who is a weightlifter. A rom-com youth story of how she finds love where she least expected it.
Strong Woman Do Bong Soon: Drama about a girl who has super-strength. It's about how she takes on a serial killer. And also, finds the love of her life.
Chicago Typewriter: A heartwarming story about three friends. One is a writer in slump, one is a ghostwriter, and one is an obsessed fan of the aforementioned writer. One of the best dramas about comradeship (and romance, obviously)
Fight For My Way: A rom-com youth drama. About long time friends becoming lovers.
Defendant:
(No Romance) A drama about a prosecutor (Ji Sung) who wakes one day to find himself in prison for murdering his wife and his daughter is missing. But he can't remember anything. The drama is about how he fights the antagonist (a brilliant one, btw) and his own memories to find his daughter.
Stranger:
(No Romance) Recently finished airing and is very popular drama. You'll have no idea who's the good guy and who's the bad one. A compelling drama about murder, corruption and politics. Brilliant written and acted.
Circle:
(No Romance) A sci-fi drama. The story is divided into two parts- 2017 & 2037. Again, a brilliantly written drama.
Tunnel :
(No Romance) A drama about a detective from 1980s who time travels to the future while chasing down a culprit.
Descendants Of The Sun: if you haven't heard about it already, reaaaaally popular show. Both in S.K & internationally. Features Song Joong Ki & Song Hye Kyo (who are about to get married soon!). Drama takes place in a fictional land. The second couple is really cute too.
The Best Hit: The story about a self-centered guy who used to be a member of a popular band J2 in the 90s. he time-travels to the future, and learns about friendship and love. Never a dull moment. a fun light watch. Nothing serious going on.
Chief Kim:
(No Romance) A hilarious, hilarious drama. You'll love it, for sure! About corporate politics, but it's far from boring or uninteresting. A wacky 'villain' and even a wackier 'hero'. Even the supporting characters did a great job!
Phew, got a bit long! But hope this helps :)