For me:

Baroque:
All of Bach's violin pieces
"Air on the G String" (also Bach)
Vivaldi 4 Seasons

Classical:
Anything Mozart, but particularly his Violin Concerto no. 5 (I think no.5) it was one of my jury pieces
All 9 of Beethoven's symphonies (the first few are more classical than Romantic pieces, but I generally count Beethoven as being a Classical era composer)
Beethoven Violin Concerto
Rossini's Barber of Seville

Romantic:
Anything Tchaikowsky, but particularly his 5th and 6th symphonies, and his violin concerto.
Dvorak's "New World Symphony"
Dvorak's 8th Symphony
Dvorak's Cello Concerto
Berlioz's Symphonie Fantastique
Dvorak's Slavonic Dances
Brahms Symphony No. 1 and all of his others, but 1 most of all

Modern:
Mussorgsky's Pictures of an Exposition
Prokofiew's Lt. Kijé
Prokofiew's Soundtrack to Alexander Nevsky
Prokofiew's Communist National Anthem (forget the name, but it's my favorite national anthem)
Orff's Carmina Burana (sp)
Copeland's work is all good, well, except for the vocal things.

Plenty more, but those are a few.

Of all Bach's compulsive mathematics, I think I like the six Brandenburgs best. Still, narrowing things down to a few favorites means inevitably that a lot of Good Stuff will be overlooked.

Things you didn't specifically mention I'd like to plug:

Haydn's Symphony No. 60 ("Il Distratto")
Mozart's Symphony No. 40
Ravel's two piano concerti
Debussy's solo piano works
Prokofiev's Piano Concerto No. 3
Holst's The Planets (overwrought and overplayed, but still great fun)

Good pieces all..

I've never been a big fan of Debussy though. Impressionistic type music has always just seemed "lost" to me. I swear, opium must have had a lot to do with the way that music was composed :D

What sober person would compose "The Dance of the Faun" -- a ballet/flute piece about some half-horse, half human thing frollicing in the forest.

Well, you know, not all characters from mythology look like the Mathis Brothers. :)

Well, you know, not all characters from mythology look like the Mathis Brothers. :)

Oh, the mythological person might look cool, but a frenchman dancing around in brown tights wearing makeup is another thing entirely, wouldn't you agree? ;)

A certain Russian Faun did a bit more than 'frolic', didn't he...


My selections are generally run-of-the-mill, but here goes:

Beethoven's Sixth and Ninth

Tchaikovsy's Fourth and the Nutcracker

Bach: Kunst der Fugue, Brandenburg Concertos, organ music

Chopin's Ballades, Fantasies, Nocturnes

Walton: Symphony #1

Biber: Rosary Sonatas (introduced to me by "Master and Commander")

Debussy: La Mer

Rimsky Korsakov: Scheharazade and Capriccio Espagnol

Vivaldi: Four Seasons (and just about anything else)

Mascagni: Cavalleria rusticana (A single aria from this Opera, "Viva il vino", pulverized what had been an implacable distaste for the genre, thanks to Wagner)

Puccini

All three movements of Moonlight Sonata - Beethoven

I like "Elsa's Procession to the Cathedral". I think it's by Wagner. We played it every year in High School for graduation. We even played it for a music contest one year and moved two of the judges to tears. It will always be one of my favs.

Handel's Water Music or Holst's The Planets for me for right now. Te Deum by Mozart.
Ooh, Alexander Scriabin (anything) and Beethoven's 9th.