There are no popular songs that make me sad. Since today was Veterans Day, I played No Man's Land and The Band Played Waltzing Matilda (both Eric Bogle songs) for myself. They are sad and talk about the waste of lives in war.
My friends think it is funny since I am not generally an emotional person, but there are a few church hymns that always make me cry - Blest Are They and You Are Mine (both by David Haas) that always make me tear up.