"I'm a Scatman" by Scatman John. [link] It touches me because of what it's lyrics tell you: Your weaknesses don't make you weak. You should manipulate these weaknesses into one of your strengths as a matter of fact.
Arcade Fire- Vampire/Forest Fire: [link] It starts off slow (but still good), but it starts building up at the 4:00 mark and when it peaks at around 5:00 it's really emotional. Be careful- it's a bit indie.
Radiohead- Let Down: [link] It's depressing, but in a way that's almost melancholic. Actually most of the songs on the album are like that.
Neutral Milk Hotel- In the Aeroplane Over the Sea: [link] The dude's voice takes a bit getting used to, but the song is just so sweet and heartwarming.