I'm fond of much on Tattie Bogle's list.

Tom Anderson's Da Slocket Light & Da Auld Resting Chair are favourites, but mostly I gravitate towards waltzes when I think of beautiful tunes:

Flowers of the Thorn
Wood Duck
Penobscot Memory
Ashgrove
Ashokan Farewell (despite being played so often)

From the Irish top ten:
Planxty Irwin,
Lord Inchiquin,
Fanny Poer,
SiBehg, SiMohr

The one that brought me to tears the first few times I heard it is Brian Peters "The Twenty-Sixth of Forever" Wish I could work out how to play it myself, but I'm much more paper trained when it comes to orchestrated pieces.

Joanne in Cleveland