Beck - Everybody's Gotta Learn Sometime
You may recognize this song from the movie "Eternal Sunshine of the Spotless Mind" (one of my personal favorites)
Ben Folds - Wandering
This is one of my favorite Ben Folds songs and it just so happens that is also a very sad song.
Elliott Smith - Waltz #1
There is something mesmerizing about this song. I don't think this song would be the same without the beautiful piano.
Modest Mouse - Broke
This song is a little heavier than the other ones but it accurately fits in the category of "melancholy"