"Koppången" by Per Erik Moraeus/Py Bäckman, look for Sissel Kyrkjebö's version on Youtube

Dark Eyed Molly (Archie Fisher/Stan Rogers)

The Loch Tay Boat Song

Jane's Whistle (Anne Dodson)

Dark Old Waters (Gordon Bok)

The tune most often mentioned throughout this thread is "Ashokan Farewell". I agree, it's a gem. So is the "Eriskay Love Lilt" (Bheir Me O).