Is it biggest hits or the most important pieces or personal favorites or a little bit of everything?
No list is complete without Bach's B minor mass which is acclaimed by many as the single greatest piece of music (I don't disagree).
Beethoven and Mozart have been recognized above, but I would add Beethoven's Late String Quartets (all of them) and his Sonata for violin and piano No. 5 ("Spring") and Mozart's "Clarinet Concerto." Schubert wrote some of the greatest chamber works; this includes his Quintet (D. 956).
Certainly the 20th century deserves some recognition; how about Stravinski's "Rite of Spring," Bartok's "Concerto for Orchestra," John Adam's Violin Concerto, and Shostakovich Piano Trio No. 2?

