Mick Jagger
According to those who drove with him in London in the 1960s Rudolph Nureyev was terrifying to be driven by. I did not experience being driven by him, but in Los Angeles in the mid-1970s I was driven by Mick Jagger.

“I'm off to a rehearsal. You are welcome to come and listen. Hop in.” 

This sounded fun, I thought, and hopped in.

He got in the driver's seat, turned up the radio and we were off at a steady pace out of the Beverly Wilshire entrance. After that it was quite different. 

He liked what he heard on the radio and began to sing, at the same time increasing his speed to...I did not dare look. And being Mick Jagger, included in the singing was waving his arms, which meant that his hands were on the wheel only when it became clear to him that unless he steered the car we would hit something. This manner of driving continued for the entire ten minute journey.

Of course, the rehearsal was worth every moment of the terrifying ride.