Most achingly-beautiful music

How about Al D. and Paco D on al's Elegant gypsy; playing those two guitars?
or Cowboy Junkies, Trinity Sessions?
The Art Pepper Meets the Rhythm section isn't aching beautiful but the story of how badly he was "living" and the great recording that came from that nexis...?

Silly as it might sound, I think Andreas Vollenweider's "Behind the Wall......" is very beautiful.

In the classical realm, most anything by Mozart. I am especially fond of Piano Concerto 466k in D minor.

The two modern artists, who move me most are Alison Krauss and Norah Jones. When I want to be taken away to a world of wistful yearning, I put on Alison. For meditative relaxation, Norah's my girl.

teardrops in the rain, joe satriani

I don't think I listen to music only to be moved by it. Not always. Sometimes it is to box with the music: to understand the aim of the composer and to judge if he achieved it.
"Giant Steps" is the one that moved me deeply, though.

The Barber and Albinoni adagios
Rachmaninoff PC #2
Canon in D -- Pachelbel
Katchaturian Masquerade Suite
Romeo and Juliet -- Prokofiev
Computerwelt -- Kraftwerk
Everybody's Talkin' at Me -- Nilsson
What You Gon' do? -- Lil' Jon and the East Side Boyz
Get Low -- Lil' Jon and the East Side Boyz
Salt Shaker -- Ying Yang Twins
Still Dre -- Dr. Dre
Some Cut -- Trillville
Still Tippin' -- Mike Jones