And, to further add to Rathdown's post, members of the US Armed Forces may wear medals and decorations of some hereditary/honourary military societies, as per this law:

10 USC Sec. 1123

-EXPCITE-

TITLE 10 - ARMED FORCES
Subtitle A - General Military Law
PART II - PERSONNEL
CHAPTER 57 - DECORATIONS AND AWARDS

-HEAD-

Sec. 1123. Right to wear badges of military societies

-STATUTE-

(a) A member of the Army, Navy, Air Force, or Marine Corps who is
a member of a military society originally composed of men who
served in an armed force of the United States during the
Revolutionary War, the War of 1812, the Mexican War, the Civil War,
the Spanish-American War, the Philippine Insurrection, or the
Chinese Relief Expedition of 1900 may wear, on occasions of
ceremony, the distinctive badges adopted by that society.

(b) A member of the Army, Navy, Air Force, or Marine Corps who is
a member of the Army and Navy Union of the United States may wear,
on public occasions of ceremony, the distinctive badges adopted by
that society.

-SOURCE-

(Aug. 10, 1956, ch. 1041, 70A Stat. 88.)

-- http://suvcw.org/mollus/uniform.htm

Regards,

Todd