Most achingly-beautiful music

The cavatina from Beethoven's late string quartet opus 130 perfomed by Berlin phil with Furtwangler. Or performed by the Hungarian String Quartet.

barber's adagio is great, also the vangelis soundtrack to bladerunner track 5 (love theme). this is a great album to turn down the lights to.

Vaughn Wiliiams symphony #5 particularly the romanza section.A favorite recording is Menhuhin and the royal phil on virgin classics vc7 90733-2

Paganini Violin Concerto No 1 op.6

I must add a couple to the previous response: Allegri's Miserere, Pachelbel's Canon, Beethoven's 7th Symphony.
The emotional loading of every piece is very listener dependent, but I still find browsing through other people's postings enchanting. What a great source of ideas for expanding one's CD collection this forum is!