--King2Hearts: a bromance that will make you cry
--Panda and Hedgehog: this is actually a very flawed and pretty crappy romcom, but the bromance in it is the best part and is different than others I've seen, so if that's what you want I guess it is ok, oh, and Donghae so there's that.
--Chuno - the hottest collection of abs in all of bromance
--Flower Boy Ramyun Shop: yes there is romance, but there is also bromance!
--City Hunter: a boy and his ajusshi, one of my favorite bromances
--Jumong: if you aren't averse to 81 episodes of sageuk awesomeness, then there is some seriously great bromance here
--Emperor of the Sea (aka Sea God): see Jumong comments, only it's just 51 eps of awesome bromance, of both the friend and frenemy kind
--Vampire Prosecutor 1 and 2: super-cute and touching bromance moments in this