I've heard persistent rumours that Super Junior and Big Bang do not get along (I believe I heard that Eunhyuk and a Big Bang member fought over a woman? Until the IU scandal everyone assumed the woman was Gyuri, but who knows, maybe it was IU) for years, but I have absolutely no idea if there's even an iota of truth to them or not, so take it with a pinch of salt.
Outside of that all the beef I'm aware of is k-hiphop related, with the already mentioned B-Free vs Bangtan thing and its associated diss tracks (Cypher 2, that reply track B-Free released that I've totally blanked on the name of), Dumbfoundead's general hate-on for all idols everywhere, and the Control fiasco last year.
Oh, and apparently Brian and Hwanhee had some kind of massive falling out that basically broke up Fly to the Sky for five years. I believe they've talked about this on variety shows since.
