Pyotr Ilyich Tchaikovsky is my absolute favorite, especially the 4th and 5th symphonies.
I love many other Russian composers, as well:
Igor Stravinsky, especially the Rite of Spring
Shostakovich (fifth symphony)
Prokofiev (symphonies 1 and 5)
Mussorgsky (Pix at an Exhibition, of course)
Contrasting them, stylistically speaking, are French composers
Hector Berlioz: Symphonie Fantastique;
Ravel: Bolero (which is a cliche these days, but is still very cool); and
Bizet: Carmen (an opera).
Speaking of style, I find that even if I don’t know a piece, I can usually identify the country of the composer. I have a feeling that each nation has a musical feel to it. Does anyone else feel this way?