...In case you want to find lots of classical music and won't mind parody manga, try reading Violinist of Hameln - it's about heroes playing magic music, and all the pieces played are either very famous or quite obscure. Actually, it was thanks to VoH that I discovered Holst and his Planets Suite.
I have to admit my favorite composer is Beethoven. XD I just respect the man since he composed his best piece while completely deaf. ...Though I love classical in general~
Franz Schubert - Der Erlkönig / I love how the tenor has to use three different singing voices. A light one for the boy, a deep one for the father and an airy one for the Erlkönig. The story itself is very scary, since the Erlkönig is a spirit who the boy can see, but the father cannot; the Erlkönig develops an interest in the boy and tries to coax him into coming with him... the boy doesn't want to, and eventually the spirit simply kidnaps him and it's too late that the father notices his son is dead.
Camille Saint-Saëns - Danse Macabre
Franz Liszt - Totentanz
Both of these are based around the same concept: Death playing music while skeletons of the dead dance wildly on Halloween.
Franz von Súppe - The Light Cavalry Overture / The main theme kicks in around 2:25... it's very catchy and sounds exactly like a galloping cavalry.
Julius Fučík - Entrance of the Gladiators / ...Commonly known as the circus theme...
Jean Sibelius - Finlandia / I hate it when people call
this the "Be Still, My Soul" hymn. This hymn isn't supposed to be religious... it's about Finland, our independence and national pride, not god. The hymn - and the entire piece - was written/composed as concealed rebellion toward Russia. "You were not broken by oppressors ruling; Your morn has come, o my native land." It's the most powerful thing to ever come out of Finnish music.
Vala (Oath) - not exactly classical, but this song is the Finnish military oath and soldiers actually have to sing it. Apparently back in 1939 during the eve of the Winter War, soldiers from Helsinki sung it while walking from their own city blocks toward the train station. As the men neared the station square, their song took an echo off the stone buildings and gained such power that the spectators' blood ran cold. "You we will protect, with our blood preserve, be without worries; your son is awake"
Edward Elgar - Salut d'Amour / Discovered this thanks to La Corda d'Oro.
Émile Waldteufel - The Skater's Waltz / I've known this waltz since I was like 8 years old. That was when I first listened to the classical CDs we have at home. (Main theme kicks in at 2:15.)
Bedřich Smetana - Moldau / I like how fast the Prague orchestra plays this... now it actually sounds like a surging river!
Oskar Merikanto - Kesäillan valssi (Summer Evening Waltz) / Finnish waltz. Merikanto was only 15 years old when he composed this.
Erkki Melartin - Prinsessa Ruususen häämarssi (Sleeping Beauty's Wedding March) / The most popular wedding march in Finland, even outdoes Mendelssohn's infamous march. My parents actually had this one at their wedding, and I'll also use it if I get married. Who would have thought a Finnish man could make something this beautiful... *pause* OK, I'm listening to everything by Melartin now. His symphonies sound amazing.
Georges Bizet - L'Arlesienne ~Farandole~
Paganini - Rondo la Campanella
Vittorio Monti - Czardas / Sounds like Hungarian gypsy music, it's just the composer was Italian. The tempo picks up at 2:09.
Antonin Dvorak - Slavonic Dances / Dance 2 is usually the one people are most familiar with. My favorite is 8. (I would have linked his "New World Symphony", but that's really mainstream... XD)
Carl Maria von Weber - Der Freischütz ~The Huntsmen Chorus~
Stravinsky's "Firebird" and Mussorgsky's "Night on Bald Mountain" are some of my favorite Russian pieces. ...I've always been scared of the latter, ever since I saw Disney's Fantasia when I was 6. XD It's been 22 years...
And this is just scratching the tip of the iceberg.