1) Healer and Hello Monster (Action-Romance kind of dramas)

2) Personal Taste and Playful Kiss (Dramas where main characters are forced to live together due to circumstances) 

3) Doctors and Descendants of the Sun (Medical Drama with lots of romance and action; medical genre is not that necessary)

Ummm if u liked healer, you could try I remember you and Love me if you dare, there both action,romance and crime
You could give a chance to It's Okay, That's Love? The main leads did have to live together for a while. However, that's not the main focus of the drama and I think it's more mature than Personal Taste and Playful Kiss (I have seen neither, but as far as I know, Playful Kiss is meant to be a cute and fluffy drama? It's Okay That's Love feels very real, very adult-like and it contains several very important matters of the real life).
1. (+1 Love Me If You Dare)
City Hunter
The Girl Who Sees Scents
You're All Surrounded

2. Full House
Just You (Taiwanese drama though)
Once Upon a Time in Saengchori (not just the two leads living together, the whole office does)
Shoot For The Stars
(+1 It's Okay, That's Love)

3. D-Day
Yong Pal
Blood
Doctor Stranger
Faith
For dramas where they live together, there's also: My Girl, Mask, Another Oh Hae Young (They don't really live together, but their rooms are connected by a door), and Prime Minister and I.
For action-y dramas, there's: King2Heart, Cruel City, and Gu Family Book, and 38 Task Force. For medical dramas maybe try Beautiful Mind.