When I was a teenager I first discovered Debussy and opened my ears to a whole new way of listening to music... I'm not even sure what prompted me to purchase some bargain cassette of Debussy's Nocturnes (side 2 had Ravel's Bolero which was another lovely surprise to my budding ears).
Whether its orchestral music, music for piano or chamber music, what is always so striking to me about Debussy is that it is such colourful music, which of course is also in part to his unusual harmonic language-- where chords sometimes cease to be "functional" but are there strictly for the sound-- there is something very sensual and even erotic I find in Debussy's music.
Back in the summer of 2006, I went on a big Debussy spending spree (I do these obsessive things from time to time LOL) and bought up at least one good recording of each of his major compositions, as well as a few not-so-well known ones. But it took me till then to listen to his one opera, Pelleas et Melisande, which totally blew me away! I am not a big opera listener, but this was an emotionally overwhelming experience for me (I went on for a couple weeks listening only to Pelleas).
If you intend on seriously getting into Debussy, the following are ESSENTIAL compositions:
The Afternoon of the Faun (this piece never ceases to amaze me)
Symphonic Sketches from The Martyrdom of St. Sebastien
Danse sacree et profane for harp and strings
And Claudio Abbado has done a concert suite from Pelleas et Melisande which is good as well
The Preludes (one of the greatest works of the 20th century for piano)
Suite Bergamasque (especially for the lovely Clair de lune)
Syrinx (a short piece for solo flute)
Sonata for cello and piano
Sonata for flute, viola and harp
Sonata for violin and piano
La Damoiselle elue (for soprano, chorus & orchestra)
The Martyrdom of St. Sebastien (a dramatic work for soloists, chorus & orchestra)
Pelleas et Melisande
And I'd recommend watching DG's DVD of the opera as well, with Boulez conducting.