Someone’s been looking at Dave Berg.
Mozart:
Piano concertos, especially #'s 10, 20, 21, 23, 26, and 27.
Sinfonia Concertante in E-Flat Major (K364 - we have a poster by that name!)
Mass in C-Minor
Requiem
I’ve been listening to this stuff for over forty years. I can’t tolerate hearing any of Beethoven’s symphonies any more. (I’ve worked in the art music field and I am NOT the only person who says this.)
Y’know what Beethoven I’ve NEVER gotten sick of, though? The A major violin sonata #9. The “Kreutzer.” I’m listening to it right now. The first movement never fails to snap my stix.
His late string quartets, too.
I’ve been listening to this stuff for over 60 years, and there’s not one piece that I’ve ever gotten tired of hearing.
Yes, the Italian Symphony is one of the greats! Also, his violin concerto in e.
The first movement of the Fifth? Really?
Really. I can listen to music as if I’d never heard it before. Plus . . . there is so much that I enjoy, that I don’t listen to any one piece very often.
I have many favorites. Here are just a few.
Beethoven: Symphony No. 9
Debussy: Nocturnes for orchestra - YouTube
Ravel: Daphnis and Chloe (ballet music). The final section (opens with “Daybreak”): Ravel Daphnis et Chloé - Suite No. 2 - YouTube
Ravel: Shéhérazade (song cycle) - #2: La Flute Enchantee; #3: L’Indifferent (lyric translation in “show more”) Scheherazade, E Parcells (2 of 2) - YouTube
Holst: Choral Hymns from the Rig Veda, Group 3, for Women’s chorus and harp Holst Hymn from the Rig Veda No.3.wmv - YouTube
Wagner: Overture to “Tannhauser” Richard Wagner "Tannhäuser" Chicago Symphony Orchestra Sir Georg Solti - YouTube
Wagner: Overture to the opera “Parsifal” Herbert von Karajan: Wagner - Parsifal, 'Overture' - YouTube
Orff: Carmina Burana - the whole thing. STAGED! very bawdy and funny! with English closed captions! Carmina Burana , Carl Orff (Ponnelle) - YouTube
Search for “classical” in Cafe Society thread titles for lots of recommendations.
Bach:
Concerto for Two Violins 1st movement - 2nd movement - 3rd movement
Violin Concerto in E Major - YouTube
Brandenburg Concerto No. 2 J.S. Bach - Brandenburg Concerto No. 2 in F major BWV 1047 - YouTube
Cantata No. 29 - (listen to the first 7 minutes) http://allofbach.com/en/bwv/bwv-29/detail/
Fantasia and Fugue in G Minor (“Great”) http://allofbach.com/en/bwv/bwv-542/detail/
Also very informative and entertaining are Leonard Bernstein’s Omnibus programs at Snagfilms http://www.snagfilms.com/search/?q=bernstein+omnibus
Also Bernstein’s Young People’s Concerts on YouTube (all in multiple parts) such as
What is Classical Music (part 1 of 4) - YouTube
Also on YouTube, his Harvard Norton Lectures Google
Another vote for Pictures at an Exhibition. I have (at least) 5 different recordings of it, including the Emerson, Lake and Palmer version and the Tomita version.
Tchaikovsky’s 4th Symphony,Finale, allegro con fuoco
You know you’ve been watching too many cartoons when all you can think of when you listen to the Overture to Tannhauser is this:
Missa Solemnis (Beethoven); B-Minor Mass (Bach); Dvorak Requiem; Turangalila Symphony (Messiaen); Grosse Fuge (op. 133) and String Quartet, op. 132 (both Beethoven); Haydn string quartets, op. 20 (really, almost any Haydn string quartet or Schubert string quartet); Schubert string quintet; Bach cello suites 1-6; Bruckner symphony #8; Schumann “Fairy Tales” (opus 132); Mozart string quintets, especially K. 516 + 593.
2 can’t-go-wrong composers: Gesualdo and Byrd
Oh crumbs, thousands of pieces I like.
If you’re exploring, try:
(these are in chronological order, but sample as you will -they should all be on Youtube)
Bach: Double Violin Concerto
Mozart: Piano Concertos No 21 and/or 23
Schubert: “Death and the Maiden” String Quartet, and his Octet
Mendelssohn: Octet
Saint-Saens: Organ Symphony
Sibelius: 5th symphony (or the 2nd)
Stravinsky: Rite of Spring
Also, there are lots of podcasts, recorded concerts and request programmes at www.bbc.co.uk/radio3
I never thought to include organ music, but there’s a ton of great stuff out there, including:
Louis Vierne: Carillon de Westminster
César Franck: Pièce Heroïque
J.S. Bach: Sleepers, Wake!
Marcel Dupré: Cortège et Litanie; Vêpres du Commun de la Sainte-Vièrge
Charles-Marie Widor: Symphony for Organ no. 5
Jean Langlais: Chanson de l’Eglise Eternelle
The compositions of Langlais are fascinating, meditative, trancelike. He included bird calls, bits of Tantric chant, and other assorted sources to create some of the most original and divine music ever written for the organ. Plus–the one thing no one knows about me–He had dinner with us at our house! (My dad was an organist and choirmaster, and Langlais was on tour in the U.S. I was only a toddler, but my parents say he adored me.) 
Not that I’m braggin’ or nuthin’, just sayin’.
Oops, messed up, it wasn’t Langlais but Olivier Messaien, and the pieces are: Apparition de l’Eglise Eternelle and *L’Ascension. *For Langlais I should have written Trois méditations sur la Sainte Trinité. My bad.
Messaien was the guy who used the bird calls and chants in his pieces.
Anything Rachmaninoff, especially the piano concerto #2.
Mozart’s works for clarinet are all wonderful, even if you hate the high pitched reeds.
Stravinsky’s Firebird Suite.
Depending on how you define classical, most Aaron Copland is very accessible. I especially like Fanfare for the Common Man.
Personal favorite: Moonlight Sonata (Beethoven).
Personally, I don’t care for Bach or Brahms.
I, too have many favorites, but this one is way, way up there. When that organ kicks in in the 4th movement…wow. It also has special meaning to me b/c my father (who was a great friend to me and died way too young) was an organist. The first concert he took me to (I must have been 5 years old) was Virgil Fox.
Anyway, my dad introduced me to Saint-Saens’ organ symphony and I tear up every time I listen to it. In fact, I’m tearing up a bit now…
Sheep May Safely Graze by J.S. Bach. Preferably as a piano solo.
Ouch.
Brahms: not even his late piano pieces? His works for clarinet (trio, quintet, sonatas)? The violin sonatas? The cello sonatas 
?
Bach: not even… everything 
?