Brisbane are hated by pretty much every other club and I can think of a reason to get all rivally with most teams (I admit some are tenuous):
Canberra - They've had a couple of shock wins against us including our biggest ever defeat. Fellow 1-city team. In the early 90s it was a real shame Canberra and Bris didn't play off in a GF.
Bulldogs - 1998 GF, 2006 Prelim, rich like us, lots of fans in Bris so they bring home games to Lang Park
Sharks - Super league GF, they've also knocked us out of at least 1 finals series. No real hate for the Shire boys I spose.
Titans - upstart chumps from down the road, motherf**kers usually push us to the limit. Still they're our bitches.
Manly - First ever match was against Manly. Everyone hates Manly. Robbed us of a fairy tale finish for Locky although they needed us to do it for them.
Storm - Genuine rivalry I feel. Qld v Qld, fellow 1 city team, both clubs mere zombie pawns in Rupert's Evil Empire. Oh and they usually beat us. Oh and 2006 GF.
Newcastle - Current version of Newcastle debuted the same year as us. f**king upstarts got all happy with their win in that little comp they had going in 1997, I forget what it was called. No real hatred from this side although I'm sure they haven't forgotten round 11 2007 where we just got away with a close win, 71-6. Newcastle also handed us our worst ever collapse when they scored 22 unanswered points in the second half in 2000 to win a game.
Warriors - Always seems to be a little more whack in the tackles against the Warriors. Ex-Bronco Campion using Webcke's head as a punching pad springs to mind. In my mind there is a genuine rivalry here although the flavour of the rivalry is not really hate. Hard to explain but I always look forward to these ones.
Cows - Qld v Qld mk II. We bashed these merkins so often for so long that for a time it was almost shameful to cheer the Broncs against them. However lately the Cows have shown they're pretty much our equal. Matches with these 2 teams is a great way to start the NRL season. Can't really hate them but sure do like beating them.
Parra - Somewhat manufactured rivalry on the back of the supposed mutual animosity between Smith and Bennett. In 2007 they scored 68 against us which I think is the record for the Broncs. I think fans of both clubs relish victory over the other although lately some of the life has gone out of it because... well, you know.
Penrith - Peter Wallace's field goal is a painful memory, so painful we poached that motherf**ker and turned him into a SOO player. The Panthers had the last laugh though when they swapped Petero for f**king Joel Clinton. No real hate against the Panthers probably.
Souths - lol@50uff$
Roosters - Genuine competitive rivalry. The Good Friday thing was great while it lasted, especially when played in Sydney, not sure why they stopped it. We love beating the Chooks and they love beating us. I mean, Brisbane vs Sydney mang, what more do you want? When Gould was in the background at the Chooks it added more spice to the dish. f**k the Chooks.
Dragons - Got to be our number 1 rivalry, surely. First you have the back-to-back GFs with Allan Langer singing a lovely little song that's still remembered. Second, they are 1 of only 2 teams that we have a negative win/loss against (the other is Melbourne). Third, there was a time for a number of years where we were to St George what St George are to Canberra. f**k it hurt watching the likes of Ryles walking off Lang Park laughing at our heckling and pointing to the scoreboard. f**k THAT! Death to the Dragons!!
Tigers - meh.
