There was a time in the late 90s when I actively sought to identify many of the classical themes and melodies that get used in our culture constantly.  A website I frequented during that time was the Classical MIDI Archives, a huge database of MIDI sequences of classical pieces.  Granted, I was only using some crappy old Sound Blaster sound card at the time, so theses MIDI files never sounded all that great.  But if the sequences were accurate enough, it was still a great way to learn just who composed all of those pieces and what they were called, and to discover new works that I'd never heard before.  At some point the site got gutted due to copyright issues, so it became much less effective.  But it is still a useful reference tool.

One piece I stumbled upon in this manner was "Vltava" (or "The Moldau"), the second of the Ma Vlast collection of symphonic poems by Bohemian composer Bedrich Smetana.  This became one of my very favorite classical pieces, and remains one to this day.  And to think the first time I heard it it was just a series of cheesy electronic noises.

Watch a live performance of "Vltava (The Moldau)" on YouTube.  Part 1 - Part 2

Wikipedia blurb