Nominations?
“Va Pensiero”, from “Nabucco” by Verdi. This piece can literally bring you to tears, particularly when you know that the people of Florence loved it so much that they lined the streets upon Verdi’s death and sang it as his procession passed by.
“Ode to Joy” would be an obvious choice.
Personally, I like Bach’s “Air for the G String.”
The critics’ choices, the Citizen Kane or Anna Karenina of the classical music world, would be Beethoven’s late string quartets.
My personal choices would be Beethoven’s Grosse Fuge ( part of one of the above), Schoenberg’s Verklärte Nacht and Britten’s Serenade for Tenor, Horn and Strings.
In the same way that the best bit of popular music is either Bohemian Rhapsody or Yesterday because of popular opinion (not mind - I can’t stand either) you dont’ wanna be going for critics’ choice.
My bet is on Barber’s Adagio for Strings or Beethoven’s 5th. Good tunes, is Beethoven’s case, great opening riff. All good stuff!
Mozart’s 40th is the greatest “classical” piece I can imagine; as for the greatest Baroque piece or Romantic piece…oh sh*t, I’m nit- picking again.
I second Bugnorton. Welcome to the boards, BTW. Haven’t seen you around before.
Nominations? Plenty. Choice? Impossible
My subjective list of 14 most important composers, with their best work (in more or less consecutive order):
Bach - Cello sonatas
Mozart - Clarinet concerto
Beethoven - Symphony 6
Schubert - String quintet
Mendelssohn - Violin concerto
Brahms - Ein Deutsches Requiem
Dvorak - Symphony 9
Wagner - Der Ring der Nibelungen
Bruckner - Symphony 9
Mahler - Kindertotenlieder
Debussy - Prelude a l’apres-mid d’un faune
Strauss R - Vier letzte Lieder
Stravinsky - Le sacre du printemps
Shostakovich - String quartet 8
Well, the UK radio station Classic FM holds a yearly poll and this year’s favourite is Rachmaninov’s Piano Concerto No 2 in C Minor.
Personally, I go for Handel.
Toccata and Fugue in D Minor by Bach. I have simple tastes.
Mozart’s Requiem. As has been said, merely a nomination – a consensus on “best” is beyond hope. Beethoven’s 9th has already been (obliquely) mentioned. For Bach, add the B Minor Mass and the St. Matthew Passion.
Second on Handel for “Water Music”.
Bah, disconnect between mind and fingers - that should be Cello suites.
I’ll nominate Mozart’s String Quintet in G minor, K. 516.
Bedriech Smetana’s Moldau - Mein Vaterland. Absolutely beautiful.
Running a close second is music from Orff’s Carmina Burana and Bach’s Jesu Joy of Man’s Desiring (not the proper Bach title, but I can’t recall it). SO wants Canon in D when I walk down the aisle at our wedding, but I’m trying to convince him to use JJOMD since Canon in D is so overused.
Ava
Oh! And how could I forget - the second movement of Dvorak’s New World Symphony. That HAS brought me to tears several times.
Ava
Beethoven’s 9th.
But only if you take the WHOLE SYMPHONY into account. The entire symphony is a masterpiece. It’s a shame more don’t hear anything but the ‘Ode to Joy’ movement, which IMHO isn’t even the best movement in the symphony.
Wow that’s a big questoin, I wouldn’t even know where to start in trying to decide what the best piece of “classical” music is, and I’m by no means an expert. I’ll just present a short list of works that I think are worthy of consideration.
Stravinsky - * The Rite of Spring *
Carl Orff - * Carmina Burana *
Dvorak - * From the New World *
Gershwin - * Rhapsody in Blue *
Holst - * The Planets *
Shoenburg - * String Quartets *
I am, of course, leaving out a large number of truely great pieces with this list, in fact I kind of feel guilty but this is what I can think of (and spell) off the top of my head, and I don’t feel like getting up and digging through my CD collection right now 
I’ve got no answer for the “best” piece. I believe the genre is way too varied and has lasted too long to decide on one piece that trumps all others - that idea just doesn’t make sense to me.
But! I can offer favorites like everyone else has, and will offer them with the caveat that they are, of course, subjective opinions (yeah, even to say “it’s tightly written, and has genius counterpoint!” seems to be subjective to me - someone can always come along and disagree with that!):
Beethoven - Symphony #7
Mahler - Symphony #9
Stravinsky - Rite of Spring and Symphony of Psalms
Ravel - Daphnis et Chloe (complete ballet)
Schoenberg - Moses und Aron
Mozart - Symphony #35 “Haffner”
Wagner - Tristan
Shostakovich - Symphony #15
Schubert - Arpeggione Sonata
Bach - Cello Suites
Bruckner - Symphony #8
…and now I stop, because I’ll just keep going otherwise 
Hey everybody–these are probably all public domain, does anyone know of a website where a good collection of classical music can be DL’d?