Ok, neither were technically banned but both the Beatles and Elvis had records burned. The Beatles for John's misunderstood statement "We're more popular then Jesus now." Elvis for thrusting his pelvis (although anyone listening to the records would not have seen his hips moving.)
Elvis was filmed from the waist up on Ed Sullivan, for that reason. The Doors were told they had to change "Light My Fire", to "Girl, we couldn't get much better". Of course, it didn't occur to them that on live TV, Jim Morrison could sing anything he wanted during the broadcast, despite what he may have sung in the dress rehearsal!

Rich