Luffy vs Akainu Akainu killed on of our favorite anime characters of all time, who is Luffy's brother, in front of him. although this fight hasn't happened there is a lot of hate between them.
Pain vs Naruto Pain is most likely Naruto's most hated rivalry (before they became friends) considering he killed Jiraya who is both their teachers, blew up his village and killed many of his comrades and struck down his future wife in front of him pulling out Naruto's hate
Igneel vs Acnologia Acnologia killed basically all the dragons. Igneel is the most powerful dragon and waited inside Nastu to take on Acnologia and kill him for what he's done.
Eren vs Annie The only 2 human Titans we know so far. Annie decided to betray her race and kill humans. Eren on the other hand want to slaughter all titans and protect the humans. Annie and Eren, as it looked, were kind of close until they went there separate paths in the army. Annie then betrayed her race and Eren was forced to fight her
Goku vs Frieza This goes way back in one of the most epic rivalries. Frieza basically killed all the Saiyans only leaving a hand full. Later on Goku and his team fight Frieza and Frieza kind of wipes them all out. After killing krillin like nothing Goku goes SSJ and we know what happened from there
Ichigo vs Ulquiorra This is my favorite. This rivalry started when Ulquiorra first went to earth and saw Ichigo and called him trash and ichigo was no match for him. About 100 episodes later Ichigo fights him again and loses. And then after about 60 episodes Ichigo challenges him again and it was a back and forth fight. This was truly one of my favorite fights.