How many Fleet Admirals has the Navy had and who were they?

If you are referring to the rank of "Fleet Admiral of the United States Navy", which is the equivalent of a 5-star general, then there have been only 4 in the history of the US Navy (many more in other country's navies):

• Chester Nimitz
• William Leahy
• Ernest King
• William Halsey

George Dewey was promoted to "Admiral of the Navy" in 1903 (in recognition of his service in the Spanish-American War), which technically out-ranks the "Admiral of the Fleet", but it is a historical anomaly.

See the link below for more information.