The one I really like is "Da Day Dawn" - a tune that comes from the Shetland tradition of playing it around the streets of Lerwick as the New Year comes in. But it has had words set to it by Jane Hazelden, and you can hear it here, sung and played (on fiddle) by Mairi Campbell of The Cast, accompanied by her husband, Dave Francis (guitar). To hear the tune as a solo instrumental, check out Aly Bain on Youtube.

http://uk.myspace.com/mairicampbelldavefrancis

"Deck the Halls" is as much about New Year as Christmas (or Yuletide, so you could probably do that one too.