Jeff Buckley's rendition of "Hallelujah" will make me practically sob every single time I listen to it. It's like kryptonite.
Also, The Decemberists' "The Crane Wife 1 and 2" and "Sons and Daughters" and "The Infanta" and "The Bagman's Gambit" and "Eli, the Barrow Boy" and... oh, hell, just say a crapload of Decemberists songs. And about half the Cure's Disintegration CD. And a lot of stuff by Arcade Fire.