This song is from the movie "Once," which I've never seen. But I did see this song performed live at the Oscars. It won an Oscar, as it should've. This version is performed by The Frames, which is Glen Hansard's band. The soundtrack version, found here, is performed by Glen Hansard and Marketa Irglova.
American Idol folks might recognize it from when Kris Allen performed it.
I could listen to all three versions of this song over and over and over and over... and might.