After the Storm - Mumford & Sons
Ghosts That We Knew - Mumford & Sons
I of the Storm - Of Monsters And Men
The Enemy - Andrew Belle
Almost Lover - A Fine Frenzy
Bittersweet Symphony - The Verve
One Day - The Verve
Bulletproof Weeks - Matt Nathanson
The Animals Were Gone - Damien Rice
The Chain - Ingrid Michaelson
Coming Home, Part II - Skylar Grey
Empty - Ray LaMontagne
Full of Grace - Sarah McLachlan
Forgiven - Within Temptation
Get Up - Barcelona
Please Don't Go - Barcelona
Gravity - Sara Bareilles
Between The Lines - Sara Bareilles
How It Ends - Devotchka
In My Veins - Andrew Belle
Chasing Cars - Snow Patrol
Run - Snow Patrol
Shattered - Trading Yesterday
Love Song Requiem - Trading Yesterday
Not all of those are exactly indie songs... but they're definitely slow, sad and depressing, and I think excellent songs.