Warrior Baek Dong Soo - To be honest the plot is boring, but the bromance, action, and soundtrack are epic. It's somewhat similar to The Untamed in that it's about a two martial artists, who grow up together, but then end up on opposite sides. (Viki)
Mr. Sunshine - Like Goblin, the main relationship is a romance, but the three male leads really develop a great friendship with each other that has a significant focus. The dynamic between them is a bit similar to the bromance in Goblin, probably because it's the same writer. (Netflix)
My Mister - This is a little different, because it's actually about three middle-aged brothers. I haven't finished it yet, but so far it's living up to people's praises. (Netflix and Viki)
Man to Man - I'd say this one is equally focused on the romance and the bromance. They're a fun pair. (Netflix)
The King in Love - A bromance and a love triangle. The relationship between the two males (they've been friends forever) is as much a focus as their relationships with the female. (Viki)
Some dramas that definitely have strong friendships between male characters, but I wouldn't exactly say are focused on a "bromance:"
Six Flying Dragons - Has a number of strong relationships between male characters and is primarily focused on the relationship between Yi Bang Won and Jeong Do Jeon, but I wouldn't call their relationship a "bromance." Some of the other relationships between male characters are closer, but are technically master-servant/ruler-retainer relationships. There is one that I would call a "bromance."
Reply 1988 - I'd call this a drama about family and friendship that also has some romance. It's about five friends, four male, one female. (Netflix and Viki)
Nobuta wo Produce - I'd also call this a friendship drama. It's about three friends, two male, one female.
The Heirs - The two male leads are best friends who had a falling out before the beginning of the drama. The romance/love triangle has more focus, but their relationship is also important (also by Kim Eun Sook, who wrote Goblin). (Netflix and Viki)
