The familiar trumpet fanfare that is so associated with the Olympics (though it is NOT the official Olympic anthem) was first introduced by ABC Sports for the 1968 Winter Olympics in Grenoble, France. The title of the piece: "Bugler's Dream" by Leo Arnaud.
In 1984, John Williams created a theme for the 1984 Olympics in Los Angeles called the "Olympic Fanfare and Theme" that is now considered a powerful piece of music associated with the Olympics and almost always played complementary to Arnaud's "Bugler's Dream".
When NBC took over the US television broadcasting rights to the summer Olympics in 1988, they commisioned John Williams to compose a unique theme for their Olympic Coverage, he composed "The Olympic Spirit" for them.
In 1996, Williams composed a theme for the opening ceremony of the Atlanta games called "Summon the Heroes", followed in 2002 with "American Journey" for the 2002 Winter Olympics.
1988 Summer Olympics album
Summon The Heroes (1996 Olympics)
American Journey (2002 Winter Olympics)
All of 'em are available at Amazon.com .