The District Sleeps Alone Tonight, by The Postal Service
Hummingbird, by Wilco
Sheep Go To Heaven, by Cake
The Grey Havens, composed by Howard Shore and Sir James Galway
Title, from the Orchestrated Ocarina of Time Official Soundtrack
Explore 4, by Jeremy Soule, for Morrowind
A Thousand Paper Cranes, by Mono
This last song holds a particular significance as it's deeply tied to a certain event involving my girl and I.

There are others, but these immediately come to mind.