Keith had a hi-hat on the right side. I think you can see it clearly in studio video of “Who Are You?”, but not sure if he had it before.
Ah, well then it works well with his tom technique! So we may be on to something. 
ETA: Though I do see from this 1965 video that he did have it on the left side at least earlier on, I guess. And I see that it’s set up pretty traditionally – he is opening and closing with his foot, though in a unpredictable Keith Moon manner.
Franz Liszt. He was an incredibly gifted virtuoso, combined with mesmerizing stage charisma and style (Lisztomania predates Beatlemania by ~120 years) and composed music that no one else (at least in his time, perhaps ever) could play as written.
Les Claypool
Freddy Mercury
Aesop Rock (probably a lot of other rappers with unique cadences as well)
Norah Jones
George Jones
Art Tatum
Fats Waller
Jon Hendricks
Paul Desmond
ETA: Randy Rainbow
Art Tatum definitely influenced Oscar Peterson. Their styles were similar, and critics and fans often compared them to each other.
Lewis Carroll
Anyone try to copy Vincent van Gogh? (Asked in innocence - nobody in particular springs to my mind.)
How about Laurence Sterne?
Others:
Steely Dan
Cyndi Lauper
Depends what you mean by Great Artist:
Vivian Fisher. Number one in a field of one.
j
I was going to ask about Van Gogh, since he’s the only painter I liked, but I kinda assumed someone would have already, maybe with a bit of spin so it wasn’t so obvious.
Has anyone tried to emulate the refined distinct genius of Cecil Adams?
I have to say, that’s quite an homage.
j
Jimi Hendrix had a fairly unique guitar style. The only musician I can think of who seemed to imitate him sometimes was Stevie Ray Vaughn, who even covered Voodoo Child.
The comedian Steven Wright was also one of a kind.
Pat Flowers was a protege of Fats Waller who performed in a similar style. He was somewhat pigeon-holed and promoted as “the next Fats Waller” after Waller’s death in 1943, which wasn’t quite fair.
I would say Mitch Hedberg was pretty darned close to the same style. Even Emo Philips, though each had their own way of approaching the humor, I guess. But they all feel very closely related to me, just with different styles of delivery.
Pollock has a lot of imitators, in an “a child can splatter paint” way, but it was methodically placed and revised so it’s usually easy to tell his from an imitator’s. His are works of art.
For a while there William Poundstone was like Cecil without the snark, but what would a snarkless Cecil be?
I’m my staff reports I tried to be Cecil, but ended up being a lesser light of the Cecil Adams school.
I was going to mention Pollack. He’s the classic target of “my kid could do that” comments, but mathematical analysis has shown that his paintings are far from random but are instead fractal (and they became even more fractal in his later paintings, indicating that this was an effect he was working to achieve). Imitators can be distinguished because they lack this fractal dimension. Pollack is probably harder to emulate than a conventional painter, because it’s not intuitively obvious how he achieved his effects.
Billy Crystal, in a Playboy interview, described Margaret Smith as someone who “does kind of a Stephen Wright thing.”