King George has referred to many kings throughout history. When used, by Americans, without further reference it most often means George III of the United Kingdom, against whom the Whigs of the American Revolution rebelled.

King George I of Great Britain and Ireland
King George II of Great Britain and Ireland
King George III of the United Kingdom
King George IV of the United Kingdom
King George V of the United Kingdom
King George VI of the United Kingdom
King George I of Greece
King George II of Greece
King George of Bohemia
King George of the Duala people
George of Georgia (several)