Kasparov obviously
THE GREATEST RIVALRY EVER!!! FISCHER vs KASPAROV!!!
Kasparov and Fischer is no rivalry because as you said they never played a game against each other.
Kasparov vs Karpov is the greatest rivalry.

Fischer's genius walked hand in hand with his insanity. Kasparov's favourite chess player was Fischer.
Fischer fell out of love with chess, Kasparov did not.

it is indeed surprising to know that both fischer and kasparov forfeited the title on default due to their enemity against FIDE.So you can't say that fischer is insane just because he forfeited the title because then kasparov too should have been insane as he too forfeited the title. Even Nigel Short and Karpov left FIDE!

I agree with JayeshSinhaChess, Kasparov - Karpov is (was) the greatest rivalry. There were some others great ones of course. What would be, for you, the greatest rivalry of today?
Fischer quit before he ran out of chess mental stamina, a great disappointment that means we will never know what his true greatness could have been. Karpov exceeded Kasparov in their later years in this regard, very obvious in their final match where the quality of Kasparov's moves would decline near the end of the games. I feel sorry for Karpov as he does not get the credit he deserves with his accurate play and winning the world title by default. Kasparov in his books on world champions does not understand why Fischer made natural good moves instead of the technically best move. This is surprising because you should only make the least best move that wins the game so you can continue to play the opening for a win. Fischer demonstrated that he understood this concept, and said that an epiphany for him was when he realized that "you do not have to equalize to play for a win".
Hey guys ,fischer and kasparov are one of the best chess players of all time.It is indeed surprising that both of them never played each other.I guess if they had played each other it would have been the greatest rivalry in chess of all time. I like Bobby because he was natural ,fearless and a genius.Whom do you prefer Bobby or Kasparov.
VS