Good Songs? - Comments

Do I Wanna Know - Arctic Monkeys
By Your Side - Beachwood Sparks
Baby - Warpaint
Help, I'm Alive - Metric
The Ballad of Love and Hate - Avett Brothers
Loser - Beck

Addict with A Pen - Twenty One Pilots has a sad vibe to it. I'd recommend anything by them though.
Car Radio - Twenty One Pilots
Skinny Love - Birdy or Bon Iver both are great
Golden and What A Catch, Donnie - Fall Out Boy Those are two of there sadder songs I feel but I'd recommend any song Fall Out Boys ever written
Twin Size Mattress - The Front Bottoms
Self-Conclusion - The Spill Canvas
Remembering Sunday - All Time Low
Kiss It Better - He Is We
My Dream Girl Don't Exist - Neutral Milk Hotel
Lua - Bright Eyes
Northern Downpour - Panic! at the Disco I'd pretty much recommend anything by them.
The Day I Left The Womb - Escape The Fate
The Mortician's Daughter - Black Veil Brides
The Freshmen - The Verve Pipe
Sleeping Pills - The Brobecks
I tried to make them all sad. Sorry if you already know these songs or hate them or something.