Hail to the Chief

Grolier says, among other things:

According to The Book of World-Famous Music, Classical, Popular and Folk (1995. Dover: New York), by James J. Fuld, the music has been attributed to a mysterious "Mr. Sanderson," who may or may not be the English songwriter James Sanderson.

The words of the song (which are rarely sung, if remembered by anyone) are attributed in the book to Walter Scott. According to Fuld, the words first appeared in his "The Lady of the Lake" tune. "Hail to the Chief" was first published in the U.S. in about 1812. It was also called "March and Chorus in the Dramatic Romance of the Lady of the Lake" by a Philadelphia music publisher, according to Fuld.

Polk's wife asked the Marine Corps band to find a song to play when Polk entered the room, so that her husband could get the respect he was due. The bandleader searched for songs, and settled on a little-known Scottish march entitled 'Hail to the Chief'.

The song worked so well, it became tradition for the next 31 presidents.

Source: A White House tour guide, as recorded by the crew of National Public Radio's All Things Considered