Michael Jackson
Luciano Pavarotti
Hank Williams
Elvis Presley
Bob Marley
Frank Sinatra
Good start, but if we're talking about the Twentieth Century here, and sticking only to those with musical talent, how about we add a few more candidates from the early years, and even a later one or two:
Al Jolson
Josephine Baker
George M. Cohan
George Gershwin
Benny Goodman
Cole Porter
Irving Berlin
Bing Crosby
Fred Astaire
Richard Rodgers
Louis Armstrong
Paul Robeson
Judy Garland
Jerry Lewis
Doris Day
Nat King Cole
Tony Bennett
Bobby Darin
Sammy Davis, Jr.
Burt Bacharach
Jimmy Webb
Barbra Streisand
Carole King
John Williams
... and those are just the Americans.
I think that to be considered among "greatest entertainers", you have to have more than one "entertaining" talent, you have to make money at entertaining, your work has to reach across generations and national boundaries, and perferably your work has to have some historical significance to it, too, in terms of being the first to do something, or in particularly influencing a style or a genre.
Singers who are composers, singers who are dancers, singers who are actors, composers who are conductors, actors who can sing -- people whose work turns up again and again in the fabric of our lives, even if they have been dead for decades.
If I had to choose just one, I think I would pick Sinatra. He was a gifted singer, had mesmerizing stage presence, and was a talented actor as well. He was also an innovator who did many new things with phrasing and arrangements that would change popular music in a lot of ways for decades after his peak popularity. He essentially invented the Vegas style (whether you like it or not, you have to recognize that it was innovative.)
Also, I'd personally like to throw out the idea that the "Greatest Entertainer of the 20th Century" just may have been a comic. Appreciation of music is always highly coloured by what style one likes, but comedy is less so (except of course for the issue of whether or not blue humour or insults are funny.)