There's a subtle difference between hatred & rivalry.
As far as hatred is concerned, teams that were hated/despised changed from
Manly in the 80's, followed by Brisbane. Manly had a resurgence mid 90's, but since then have fallen back with lack of success.
Canterbury & the Roosters have since raised the Ire of many a league fan, and (along with the ever-present Broncos) taken the mantle of the despised teams in the competition. But you can't say that all teams would have a rivalry with the Bulldogs/Roosters.
Rivalry isn't general like hatred and they don't always go hand-in-hand. It usually stems from a history of bitterness, jealousy, intense competition, amongst others. But most of all its the local rivalry that is biggest of all.
Of the rivalries in League, the biggest one is NSW vs QLD. At Club level...
Dragons vs Sharks
Roosters vs Rabbitohs
Eels vs Panthers
would have to be the biggest three - local rivals.
Others I know of include
Sea Eagles vs Knights (from the 97 GF. Manly fans I know - and I know plenty - hate the knights with a passion - stemming from positive drug tests by the knights the following season)
Manly v Parra - obviously from the 80's
Manly vs Cronulla - from the 70's
Dragons vs Broncos - from the Early 90's
Dragons vs Rabbitohs
Dogs vs Eels
Dogs vs Dragons
and in years gone by, the biggest of them all had to be the Fibro's vs the Silvertails - Wests and Manly. This was Hatred & Rivalry at its most intense. Players, Coaches, Fans, they all detested each other. Some of the stuff that went on in these games of the 70's, 80's was incredible.