Also "Shamandalie", "My Selene", and (if you pay attention to the lyrics), "Paid in Full". All awesome, all will bring you to your knees if you let them.
"Tallulah". Listen to it after a breakup! Yeah, a breakup song after a breakup is extra tearjerking as it is, but Tallulah tops them all. Now listen to it after a breakup when neither of you wanted to break up - but you did, because you wanted your ex-significant-other to be happy and you knew that she couldn't be happy with you anymore. And you know that you could practically undo it with a phone call. But you still don't do it because you want her to be happy.
"Draw Me", "The Last Amazing Grays", and "Replica"
"The Day" from Stones Grow Her Name. A man loses his family in a flood but handles it with a dignity that will have listeners scrambling for hankies.
Not just any flood, mind you, but the tsunamis that struck Japan in spring 2011.
You can add "Replica" to the list as well.
A new album means new tearjerkers. From Pariah's Child, the song "What Did You Do in the War, Dad?" about a father who did terrible things he thought would make the world better for his children, but now is haunted by his dark past and unable to enjoy being a parent.
Basically, what we're saying here is that every album has a couple. At least...