'Everything changes' by Staind is not exactly a sad song to most people because they haven't gone through what the song is talking about. But I have, so yeah, the song does make me emotional when I listen to it.
'No one there' by Sentenced is also a very sad song. It makes me think of my grandfather who is having non-stop health problems. Very emotional song there. I also find 'Hands held high' and 'Shadow of the day' by Linkin Park very moving songs.