Recommendations

Prequels & Sequels of each other!
There are 2 volumes in the "Three Lives, Three Worlds" series!
"Ten Miles of Peach Blossoms" & "The Pillow Book"!
The second book focuses on Fengjiu & Donghua!
Same actors/actresses!

Similar in: vampires stories, predestined love, love story over centuries, modern setting with fantastic creatures.

A girl from the present world is able to travel back in time while her current life is a mess. Whereas in the past she finds a place where she finds her self more at home in the past than in the future.

Both dramas have incredibly intelligent psychopathic serial killers (especially Gap Dong).
If you enjoy those kind of stories you will definitely like both of these dramas.
While Hello Monster has a really complex story with incredibly diverse characters, Gap Dong's story is way darker and focuses more on the nature and the perspective of the serial killer and his actions.

-----(minor spoilers following)-----

In my opinion the actors for Hello Monster were all incredibly well cast which helped to improve the story and made it easier to portray the characters. In contrary for Gap Dong Lee Joon did an amazing job on portraying a coldhearted psychopathic killer, while in my opinion the other main roles were poorly cast/ badly portrayed, which didn't really help the storyline...

Both deal with North-Korea and South-Korea and show the conflict of the two countries.
While Confidential Assignment has a North and a South-Korean Cop cooperating and shows a bit of the South Korean perspective of North Korea; Secretly, Greatly deals with North-Korean Soldiers and Spies undercover in South Korea.
Both movies have amazing action scenes, a great story and are also really funny.

In both dramas the main protagonist/group are solving new interesting cases each episode.
If you like the concept and the crime genre you will definitely like both.

In Vampire Prosecutor it's a well Prosecutor who is a Vampire.
In God's Quiz the main character is a "normal" intelligent doctor, who helps solving many cases.

Similar in : interior conflict that ruined the country, usurpation by the desire of grandeur hidden under pretense of saving the people, the way of the sword chosen above anything else. Distinct filming, strong acting.

Similar story for: love loyalty emotions, plot at the palace, unfulfilled love, devotion, great endurance to grinding, also Tae Woong Uhm in equally moving role.
Moves you until you cry a river. Extraordinary performance of the actors.

Similar love story, deep, intense, devoted emotions, painful life stories, plots at the palace, always someone for their lives, tragic end. Moves you until you cry a river. Extraordinary performance of the actors.

Similar love story, misunderstandings, sorrowfull love, great feelings, both on enemies sides but fall in love, tragic end. Similar Romeo and Juliet plot.

I cannot hug you and I cannot hug you two has the same lead. They are also a sequel both of 16 episodes the sequel just continues the first season.

Both male main protagonist has germophobe they both are very clean and fear of germs. Both has a short amount of episodes and has a sequel to it.

Love story between human and robot, but different story. Both of dramas are beautiful, sad and funny in the same time.

Don't even get me started, what I can say without spoiling anything is that while watching Misty I couldn't stop thinking how similar it is to The Good Wife, it offered me the same feelings, it had the same approach of the story but different plots. Definitely check it out you won't regret it!

I feel that the male leads are similar to one another and have similar aspects. Also the whole feel/vibe/atmosphere of the drama is similar in my opinion.