I think it will be hard to find without any romance.

God's Gift - 14 Days
Little Girl K
Three Days (2014)
Two Weeks (2013)
The Village: Achiara's Secret (2015)
Ghost

and from j-drama

Ouroboros

But i assure you that you can watch everything from my list if you like thrillers
Thank you so much everyone! I'm really looking forward to trying out the dramas you recommended! =) Haha I hope that I'm someone who loves romance in my next life just because of how pervasive it always is! xxx
Confession of Murder (2012)

Comrades 
Someone suggested it before, however it has some romance in it as two ex-lovers face each other in battles (North-South) and can't kill each other, giving you replays about previous occurences between them and their thoughts afterwards for not wanting to kill each other... Not sure if it sounds correct haha, but I guess and hope you understood me, so it is entirely up to you if that's too much romance already or not :) 
It's already been mentioned but I definitely recommend "Punch", though it does have quite a strong political (and so, naturally, revenge) theme. But the main actor Kim Rae Won plays his character amazingly well, as do the other main actors.
I really, really don't like watching romances and it's nearly impossible to find Korean dramas that don't concentrate on love triangles. I will try a few of the suggested shows from this thread myself.

Three more:

Flower Grandpa Investigation Unit

Shut Up: Flower Boy Band (this actually has romance, but for me it was so unimportant to the plot that I didn't mind ignoring it. It's basically my favorite drama.)

Bad Guys
Apart from the ones that are listed, Chief Kim also has no romance. 
+2 Angry Mom and White Christmas
+1 Chief Kim
Page Turner
38 Task Force
I Remember You has a little romance but nothing worth mentioning
Night Light
Signal has a romantic back story but no actual romance
+3 The Village: Achiara's Secret
Voice
It looks like it hasn't been mentioned yet so Lookout!
Tunnel. 
Defendant
My Lawyer, Mr. Jo
(the three above dramas all have an established romance or had a romance that ended in the first couple episodes then the focus is on the main non-romance plot)
+2 Chief Kim (one of my favorites~)
Last (2015) is a interesting drama with no romance and a unique plot.
I tend to lean towards dramas without romance as well!  I recommend:
Kdramas:
Ghost
Nine: nine times time travel (one of my all time favorites)
Secret Investigation Record

There a lot of great dramas outside of south korea as well.  I would highly recommend liar game (first season), bloody monday (first season), and Nirvana in the Fire!

Circle
Defendant 
Chief Kim 
Tunnel 
Two Weeks
Liar Game
White Christmas
Liar Game
Signal
The Village: Achiara's Secret
Angry Mom
God's Gift - 14 Days

Cruel City has a little romance but it isn't the main point at all and the synopsis makes it sound like a lot more than there actually is.
Liar Game, (Angry Mom?) & Nightmare Teacher.

The Lover is about different couples living in an apartment complex, but it's not that lovey dovey (Not a lot of kdrama tropes!) + BoyxBoy, haha!
Duel, Solomon's Perjury, The Chaser.