Although it's widely believed that
American military ranks top out at the five-star "
General of the Army" or "
General of the Air Force," two Americans have been appointed to the slightly superior rank of "General of the Armies of the United States":
George Washington, and
John Pershing, who commanded the U.S. force in
Europe in
World War I.
The five-star rank was awarded to Generals Dwight Eisenhower, George C. Marshall, Douglas MacArthur, and Omar Bradley in 1944 so that they'd be at least on par with British and French field marshals, over whom some of them had command.
Pershing, however, until 1919 a four-star general, was made "General of the Armies" in that year. He retired in 1924 but officially kept the rank until he died in 1948. That said, even during his five years of active service after he was awarded the rank, he never actually wore more than four stars.
The sixth star, however, became implied in 1944, when Eisenhower, MacArthur, Bradley and Marshall were promoted. At the time, Secretary of War Henry L. Stimson said explicitly that none of the new five-stars should be considered to outrank the still-living Pershing, and indeed that their rank was to be considered a separate grade from his. Ergo, the implicit sixth star.
Washington was a lieutenant general in his lifetime and was only given the "General of the Armies" designation in 1976, by an act of Congress whose purpose was to make sure that he was placed, retroactively, ahead of Pershing in the all-time rankings.
An arcane summary of army research on this subject is at http://www.perscom.army.mil/tagd/tioh/rank/goa.htm