The songs that touch me most, and bring me the most comfort are:
"A Little Rain" - Tom Waits
"Before You Were Born" - Toad the Wet Sprocket
"People Ain't No Good" - Nick Cave and the Bad Seeds
"Hallelujah" - by Leonard Cohen, covered by Jeff Buckley
"Rhapsody on a Theme From Paganini" - Rachmaninoff
"Johnny" - October Project
"All Apologies" - Nirvana
There are more, but those are the first to come to mind.