The rank of General is recognized as the highest rank in most any army of the world and almost always represents a high-ranking official who has dedicated his/her career to the military. The United States military maintains several sub-ranks within the general rank itself and this position can go as high as a "5 star general" when the situation warrants. Note that the Army rank of 5 Star General is only specifically handed out at wartime during the most extreme of circumstances as it was to the men listed below during both World War 2 and the Korean War (their awarding date follows their name). As such, you'd be hard pressed to find a living, breathing 5 star general serving in today's military (the last Five-Star rank was held by General Omar Bradley until his death in 1981).
Additionally, the U.S. Navy maintains its own "Five Star" status in the form of the rank "Fleet Admiral". This rank was awarded to the following men (their awarding date follows their name):
Only one member of the United States Air Force (then as the "United States Army Air Force") has ever held the rank of 5-star general as "General of the Air Force". Henry H. Arnold also holds the distinction as the only person to ever achieve the 5-star rank in two branches of the U.S. Armed Forces:
Of note is the grade of "General of the Armies of the United States", a position held by only two persons in American history - George Washington and John J. Pershing. Of the two, only General Pershing held the title while still alive, Washington being posthumously bestowed the honor by President Gerald Ford in 1976. Pershing earned the title in 1919 after his service in World War 1 and held it until his death on July 15th, 1948.
It also bears mention that, on March 24th, 1903, Admiral George Dewey (1837-1917) was honored with the special grade of "Admiral of the Navy" (retroactive to March 2nd, 1899) which was intended to be senior to the four-star admiral rank. Dewey remains the only US naval service member ever awarded this title. In 1944 (during World War 2), Admiral of the Navy was formally recognized as senior to the 5 star rank of Fleet Admiral.
General Ulysses S. Grant (of American Civil War fame) was given the rank of "General of the Army of the United States" by the U.S. Congress on July 25th, 1866. He wore the rank insignia with four stars and was reportedly never addressed by this title. Upon becoming President of the United States of America, the position fell to William T. Sherman on March 4th, 1869. Under Sherman's direction, the rank insignia was revised to showcase just two stars. On June 1st, 1888, the rank was passed to Philip Sheridan and its tenure ended with his death on August 5th, 1888.