Most achingly-beautiful music

Verdi's Requiem - the whole thing.

Rodrigo's "Concierto de Aranjuez" is simply The most haunting and beautiful melody I have ever heard...

Bach's "Air For the G String"

For popular music... any ballad played by the late cornetist Bobby Hackett (who can be heard on most Jackie Gleason recordings, "Music For Lovers Only", etc.)

The 2nd movement of Rodrigo's "Aranjuez" is the specific melody I had in mind. But I will shamelessly use this opportunity to mention another hauntingly beautiful melody: Massenet's "Meditation" from Thais...

...Louis Armstrong's "What a Wonderful World" on her "Live at Blues Alley" CD. Simply the most beautiful, evocative and emotionally connected vocal performance of this song that I've ever heard. Brings tears to my eyes every time. The rest of the CD is phenomenal as well.

The Marriage Of Figaro (Act 3: Duettino) Most of you remember this from the movie The Shawshank Redemption. This beautiful music was played over the prison P.A. system and brought the entire prison to a standstill, and almost created a riot.