Over a year ago I wrote about my favorite piece of music: the Meditation from Massenet's Thaïs. I just heard another lovely version of it, Yo-yo Ma on cello with piano accompaniment.
Another favorite piece is "Tu se' morta" from Monteverdi's opera L'Orfeo. This song is Orpheus lamenting that his beloved Eurydice is dead, and vowing to go to the underworld to bring her back. It ends with him singing "Goodbye world, goodbye sky; and sun, goodbye." It's just heartbreaking. You can hear it here. Monteverdi kind of straddles the Renaissance and Baroque eras, similar to how Beethoven straddles Viennese Classicism and Romanticism.
I'm linking to them because I can't embed them. To make up for this, and to split the difference between the two, here's J. S. Bach's Partita for flute in A minor. I pretty much love everything by Bach, but I think he's at his best when writing for solo instruments.