Hands down is Ali-Frazier but Barrera-Morales deserves a mention, that was some classic rivalry prolly best in lower weight division in history till Pac-Marquez trilogy happens
Ali-Frazier,in my opinion,is the greatest rivalry in sports history.Even though the second fight wasn't very good,the first and third were the best and most compelling heavyweight fights that I've ever seen.Besides the fact that Ali may be the greatest heavyweight in history,and Joe top 10,possibly top 5,those 2 battles were unmatched by any other heavyweight fight that I've have ever seen in both their action and the drama attached to them.
Whoever pick that is not name Ali/Frazier need to hit themself in the head. There is nobody and i mean nobody that hate each other more then these 2 fighters. Yes Barrera and Morales hate each other 2 but not as big as Ali and Frazier. Bowe and Holyfield never hate each other. Gatti/Ward never hate each other. Marquez vs Vasquez never hate each other. Maybe Leonard vs Hearns but is still not close to a real rivery of Ali/Frazier.
Ted 'Kid' Lewis and Jack Britton deserve a mention from the old timers, fought each other about twenty times, some of them times for the World Welterweight Title. They hated each other as well.
It's the GOAT vs Smokin Joe but those Vazquez vs Marquez fights some of the best action you can get. The Gatti vs Ward 1st fight transformed me from a boxing fan to fanatic.