If by "famous" you mean the feud that the most people knew about, it would probably be Ali vs. Inoki. But if you're asking which was the biggest feud within wrestling circles, that's totally a matter of opinion. Jumbo/Baba vs. Hansen/Brody, maybe?
I have lot all my respect for my namesake...there I would like to be known as WilliamsFan from now on...I feel disgraced with the name of Edge on me...
I kinda recall we had another thread like this but I couldn't find it.
Anyway, many feuds involving Rikidozan is very famous and historically important. To list a few:
Rikidozan vs. Fred Blassie
Rikidozan vs. Thesz
Rikidozan vs. The Destroyer
Rikidozan & any partner vs. The Sharpe Bros
New Japan:
Inoki vs. Tiger Jeet Singh
Inoki vs. Stan Hansen
Inoki vs. Hogan
Inoki vs. Rusher Kimura
Fujinami vs. Choshu
Tiger Mask vs. Dynamite Kid
Tiger Mask vs. Kuniaki Kobayashi
All Japan:
Baba vs. Abdullah the Butcher
Baba vs. Hansen
The Funks vs. Sheik/Abdullah (possibly the most important feud in the history of All Japan)
The Funks vs. Hansen/Brody
Tsuruta vs. NWA/AWA world heavyweight champs (mainly Race, Bockwinkle, and Flair)
Tsuruta vs. Brody
Tsuruta vs. Tenryu
All Japan Women's:
Beauty Pair vs. Black Pair
Jaguar Yokota vs. Devil Masami
Crush Gals vs. Dump Matsumoto & Bull Nakano
Gotta be more, but that's all I can think of in this Saturday morning...
During most of the JWA days, it was usually Japanese (faces) vs. gaijins (heels). The feud between the Funks and Abby/Sheik changed that the gaijins can be super faces. In early 80s, Dory Jr. and Terry were even more popular than the Japanese team of Giant Baba & Jumbo Tsuruta. They even had a group of cheerleaders in the arena (consisted of the fans, not planted) for Terry.
During most of the JWA days, it was usually Japanese (faces) vs. gaijins (heels). The feud between the Funks and Abby/Sheik changed that the gaijins can be super faces.
I'm not so sure if it was really the Funks that changed that, however. Destroyer was an extremely popular babyface in 1973, 4 years before Dory and Terry officially "turned" during their feud with Abby and the Sheik. Also, Billy Robinson was often booked in All Japan as a face as well, he certainly got a large amount of cheers and a sympathetic angle in his feud against Abdullah in 77.
I'm not so sure if it was really the Funks that changed that, however. Destroyer was an extremely popular babyface in 1973, 4 years before Dory and Terry officially "turned" during their feud with Abby and the Sheik. Also, Billy Robinson was often booked in All Japan as a face as well, he certainly got a large amount of cheers and a sympathetic angle in his feud against Abdullah in 77.
You're right that the Funks may not have actually "changed" that, but unlike The Destroyer, who actually lived in Japan and was a full time member/employee of All Japan, the Funks didn't really have to "side" with the Japanese to become the faces.
That is certainly a valid point. I just always saw the Funks' face turn and them being embraced by AJ fans as a part of a progression started by the Destroyer, who was well liked and somewhat of a cultural phenomenon even as he worked heel in the JWA because of his charisma and comedic timing.