I will tell you that I'm not that experienced with classical music (much more of a rock/metal/punk guy)...but there a few select pieces of classical music that are absolutely mind-blowing.
The first is "Night on Bald Mountain" by Mussorgsky (although I believe the more well-known versions of this was a reworking of the original by Rimsky-Korsakov).
Either way - I think it's a great first piece of classical music to get into - it's relatively short & easily digestible - and stunningly beautiful.
I haven't tested the link - but I think you can hear it here:
http://www.musopen.com/view.php?type=piece&id=178
The other is the Symphonie Fantastique by Hector Berlioz. Still very popular & widely performed. You've heard pieces of it if you've ever seen the movies The Shining or Sleeping with the Enemy.