Gong Yoo and Lee Dong Wook in Goblin
Misaeng (Incomplete Life): Between all the main characters.


Lee Jong Suk and Kim Woo Bin - School 2013
Park Hae Jin and Seo Kang Joon - Cheese in the Trap
school 2013
protect the boss
Warrior Baek Dong Soo
East of Eden 
Can You Hear My Heart 
A Gentleman's Dignity 
High Society 
King2Hearts
Man to Man
movie : No Breathing 

jdrama Gokusen 2 : Ryu/Yabuki
Main characters on man to man XD
"Tunnel" has a great Bromance
I will add "Duel", this Drama is excellent ! Jang Deuk Cheon and Lee Sung Joon  have some kind of bromance
Goblin & Grim Reaper (Goblin)
TQ's Psycho & Gluttonous Sociopath (Chief Kim)
Han Se Ju & Yoo Jin Oh (Chicago Typewriter)
The Disguiser
Goblin
Nirvana in Fire
Chief Kim
Sungkyunkwan Scandal
Warrior Baek Dong Soo
Oh my venus
Lost Love in Times

you asked only for kdrama but I mention c-drama too. IMO C-drama has lots of Bromance drama.
Signal
Goblin
Chicago Typewriter
Sassy Go Go
Love in the Moonlight 

I already watched a lot of brotherly love in kDramas but for me the outstanding bromance of all those came from: 


Gentleman’s Dignity - bestfriend since high school until their 40’:s.

Reply 1988  - all of them have been friends since their childhood. Even their parents were really good friends.

Ojakgyo Brothers - all of them are siblings but they treated each other as best friends.

In no particular order:

  • padam padam 
  • reply 1988
  • moonlight drawn by the clouds
  • dots
  • legend of the blue sea
  • nobuto wo produce - classic jdrama i have to throw in
  • bad guys 
  • confidential assignment - movie
  • jelousy incarnate
  • my annoying brother - movie
  • save me
  • the king in love
  • chicago typewriter


Bromances although i don't recommend the drama:

  • gentlemans dignity
  • bromance (don't let the name deceive you...really a gender bender)