Under Your Tree by Sonata Arctica is probably the saddest song I've heard that isn't a choir song. Its about a father burying his son underneath a tree he planted the day his son was born. Its a beautiful song.
http://www.youtube.com/watch?v=iFDLkIRYRYQ
Tell My Father (From the musical Civil War) is another. I sang it in a choir. Its about two brothers, one fighting on the North, the other for the South, and one kills the other. The song is from the point of view of the dying brother who is telling his brother to tell their father that he died with glory and honor.
http://www.youtube.com/watch?v=QnYOfMrpKpA (Not a huge fan of the vocalist in this rendition, but it works)
Ludo's Morning In May from their Broken Bride rock opera EP. I'm not gonna bother explaining the whole story, so I recommend Wikipedia-ing the album for the plot.
http://www.youtube.com/watch?v=NDbhf8BXLow
However, the saddest song I know is Whiskey Lullaby by Brad Paisley. Say what you want about the genre, but country, true country music, has the saddest songs.
http://www.youtube.com/watch?v=dYub1neLZmA
Those are the first four that come to mind. If I really tried, I could probably think of more.