The everlasting rivalry between the older generation and the younger generation will supercede all else.
In a literal sense, probably Kasparov-Karpov was the most intense.
The funniest was probably Alekhine-Bogoljubov, with Alekhine making fun of his opponent at any opportunity. Poor Effie...
In the history of chess, what can go down as the best rivalry ever?
White vs. Black.