Dear Lord!
Lol, I go away for the weekend and come back to enough music to probably keep me busy for months!
Thank you all for the contributions, I better get started on these before I have more music than time to listen to before I’m dead 
BWAHAHAHAHAHAHAHAHAHA!!! Sweetie, I have a Bachelors & Masters Degree in Music, and there are classical pieces that I haven’t listened to yet.
Better get going - there are some stunningly beautiful pieces out there, pieces that will make you weep, pieces that will get your adrenaline going, pieces to dream to. And thanks for asking our opinion.
I recommend:
“Pavanne for a Dead Princess” by Maurice Ravel
“Concerto No. 20 in D Major for Orchestra and Piano” by Wolfgang Amadeus Mozart
“Symphony No. 5” by Dmitri Shostakovich
“The Planets” by Holst
The William Tell opera by Rosinni
“Don Juan” by Richard Strauss
“Symphony in F Major for Piano and Orchestra” by George Gershwin
about anything by Johann Sebastian Bach
it’s not considered classical music as yet, but check out Duke Ellington’s “Beige, Brown and Black,” especially the version where Mahalia Jackson sings “Come Sunday”
Brocolli! - everyone here has given a lot of good suggestions!
My choices (I am limiting these to each of the major “periods” of classical music)
Baroque:
[ul]
[li]Bach - Brandenburg Concertos[/li][li]Handel - The Messiah, Water Music, Music for Royal Fireworks[/li][li]Vivaldi - The Four Seasons[/li][/ul]
Classical:
[ul]
[li]Mozart - Symphonies 39, 40, 41 (most of the earlier symphonies are somewhat dull by comparison)[/li][li]Mozart - Piano Concertos (#9 and up are all good)[/li][li]Beethoven - Symphonies 5,6,7,9[/li][/ul]
Romantic:
[ul]
[li]Schubert - “Unfinished” Symphony, Trout Quintet[/li][li]Chopin - Waltzes, Etudes, Ballades[/li][li]Mendelssohn - Symphonies 3,4[/li][li]Dvorak - Symphony #9 (“From the New World”)[/li][li]Tchaikovsky - Violin Concerto, Piano Concerto #1[/li][/ul]
Post Romantic, Impressionist, National Schools:
[ul]
[li]Holst - The Planets[/li][li]Grieg - Piano Concerto, Peer Gynt Suites[/li][li]Sibelius - Symphony #5[/li][li]Ravel - string quartet[/li][li]Vaughan Williams - English Folksong Suite, Fantasia on a Theme by Thomas Thallis[/li][/ul]
Gawd, there’s so much! You can’t go wrong by buying a composer’s greatest hits package and then deciding what you like. In fact, you’ll get the smaller pieces that way. My list seems to emphasize the bigger symphonic works.
Most of the stuff I would have recommended has been suggested already…Holst, Verdi’s Requiem, Shostakovich etc. But try:
-Alberto Ginastera’s Pampeana #3: Impetuosamente
-Hector Berlioz’s “Symphonie Fantastique”
-Brenno Blauth’s “Concertino for Oboe and Strings”
-Anything by George Gershwin, if you consider that classical.
-Respighi’s (Not sure of the spelling) “Pines of Rome.” You may have heard this in Fantasia 2000 by the Chicago Symphony, with their badass brass. Play the game of “Where’s Charles Vernon?” It’s a lot easier than “Where’s Waldo?”
-Neil