^^^I pretty much agree that the most influential person or group preceded anyone that we even know. But, in terms of more contemporary influence, say last half of 20th century, and Western influence since this forum has a Western bias, I believe:
Velvet Underground had most early influence on rock.
Beatles had most early influence on pop.
Bessie Smith, Robert Johnson, and Muddy Waters had most early influence on blues; Bessie Smith and Louis Armstrong had most influence on jazz vocalists; and Robert Johson had most early influence on blues rock.
Thelonius Monk and John Coltrane had most early influence on instrumental jazz and Miles Davis had most influence on later jazz and jazz fusion.
Kraftwerk had most early influence on techno/house.
Janis Joplin had most early influence on all female rock artists (probably later female pop, too).
Youssou N'Dour had most early influence on world music and introducing non-Western sound to Western music.
Hank Williams had most influence on country.