CBC Radio's Tom Allen investigates the origin of the opening four notes of the classic Star Trek theme. He traces it to the opening of Mahler's First Symphony, then further back to Brahms's Second Symphony and Beethoven's Fourth Symphony.
In college, one of my classmates (the same one that is now the conductor of an orchestra) identified the source of the trumpet fanfare in the Star Trek theme, also known as notes five through seven: Mahler's Seventh Symphony. Skip to timecode 11:05.
Eventually, we may find out where notes eight through twelve came from. If the trend keeps up, we may discover that it came from yet another Mahler symphony.