I cried when I heard the song 'Signal to Noise' (Peter Gabriel) for the first time, because of the climax with the orchestra. That was one of the most intense things in music I ever heard up to that point. I keep on playing the song to get the same kick and emotional feeling out of it, but it cannot match the first time and I never cried again.
Another one was 'Since I've been Loving You' by Led Zeppelin, just on a random occasion. And 'House of Cards' by Radiohead, when I broke up with my girlfriend. The first line: 'I don't wanna be your friend, I just wanna be your lover'. A simple sentence, not much to it. But the way Thom Yorke it delivers just made me all watery.
The weird thing is that I've never cried to a song by one of my favorite bands like DT, Porcupine Tree, Devin Townsend, Opeth etc.