Most strong unforgeteble bromances, friendship where they are ready for everything because of each other :
modern:
Cruel City AMAZING drama, bromance where they are ready to die for each other, side romance which is much better then 90% romance dramas and so many other greatness ))) p.s. ML has his love interest and friend has many ))) not even close to liking same girl.
Goblin
School 2013
Shut Up: Flower Boy Band (group friendship and I wouldn't mention it in "bros for life" but first 2-3 episodes were very emotional and one of most unusual memorable character)
Historical:
My Country: The New Age So great drama! (though for some time they both like same girl but then one of them moves on and it never was big issue or triangle. They had more political problems, they became on opposite sides and it's enemy/friends dynamic, but from almost 200 drama I've seen it's one of most strong/emotional bromance)
Warrior Baek Dong Soo could write same here, but it's not as great/high quality drama as "my country" though it has one of most unforgateble anti hero SML who is real star of the show.
Chuno it's not as great bromance as above 2 but drama has many similarities, if you will like those 2 you will like it too, but as drama Chuno is really great, better then "Warrior" but "My country" still is best.
The King in Love - it's very love triangle, but still great bromance and beautiful drama.
there are many good friendships in dramas, some are mentioned here, but I wrote only those dramas which has emotional strong focus on this deep friendship.
could also add Descendants of the Sun
But most emotional deep bromances have "My country", "Cruel City", School 2013, "warrior beak dong soo". Also "king in love", but romance/love triangle if not shadows at list is equal. "Goblin" isn't as "dramatic" but cute funny and great watch bromance.