Love me some Debussy... God, I just can't get enough of Syrinx. I don't really think the term "Classical" is good, though. When you say classical, I think Mozart, Beethoven, etc., whereas the music I like most comes from the late 19th and 20th century. Tchaikovsy is great indeed, I also love Igor Stravinsky. Gotta love the Russians when it comes to expressing emotions...
I'm also very proud of my fellow Poles when it comes to composing music. Of course, the biggest legend here is Chopin, but there's plenty of incredible 20th century music as well. Just take a listen to Górecki's Symphony of Sorrowful Songs, or Kilar's Orawa. Now, I know this is not music for everybody, but I find it mind-blowing. The use of traditional folk melodies only makes it deeper.
For even more weirdness, there's Oliver Messiaen, whom I greatly respect. The dude was a genius and revolutionized many aspects of harmony and rhythm. I cannot bring up any examples now, but I might post them later on. I encourage you to look him up, though his music might be quite difficult at times.