Most achingly-beautiful music

Barber's adagio for strings always moves me as does Pavarotti singing Nessun Dorma. What a terrific thread, I hope it runs another decade.

Carrickfergus (traditional Irish song) as performed by Van the Man and the Chieftains on Irish Heartbeat...

CSNY Cowgirl in the Sand, Neil Young doing The Needle and the Damage Done, Velvet Underground Oh! Sweet Nuthin'

Elgar's Cello concerto played by Jacqueline du Pré...

...or Bach's 5th Suite for Cello.

Something about solo cello that is brooding, haunting, and ultimately moving!

Pierre Bensusan's Intuite and Altiplanos:
Some of it literally make my eyes well up and brings on that slight hyperventilating that only something extremely moving can do. I've yet to hear anyone do (for me) what he can do with a guitar.