Question

Which 1960s band is regarded as being responsible for launching rock ‘n’ roll into the mainstream?

Answer 1

Difficult question to answer, first what do you consider to be "rock ‘n’ roll"; how to define that is hard to do.  Bill Bailey may be a starting point with 'Rock around the Clock'

Answer 2

Well, the Beatles were, by most, regarded as the most sucessful. However they were closely followed by others, such as The Rolling Stones, The Grateful Dead, The Who, etc...

However, as for which band launched the Rock and Roll industry skywards, it would have to be the Beatles. There first appearance on the Ed Sullivan Show is regarded by many as the beginning of the "British Invasion", a large scale wave of rock and roll bands from England to the USA.