-'Asleep' by The Smiths once made me start crying while in public. I'm lucky no-one else was paying attention to me!
-'Bringing the Body Back Home' by The Real Tuesday Weld is an amazing song, and one that I'll always associate with breaking down bawling in my room, a moment which finally galvanised me to later come out to my parents.
-'Konyadake' by Takkyu and Tavitz always makes my heart hurt in a good way, both from the beautiful tune and the use of it in Devilman Crybaby.
-'Good bye jonathan' by Adustam. I'm always amazed by how Adustam seems to tell stories with their music despite being almost entirely instrumental. "Lust for Summer Blues' is another beautiful song of theirs, and was used to amazing effect in the animated short 'Kanamewo'.
-Both 'Ocean Breathes Salty' and 'The World at Large' by Modest Mouth don't exactly make me tear up, but they're raw and melancholic songs from a great band.
-'White Silence' by TK, from Ling Tosite Sigure. Even without understanding the lyrics, which are tear-jerking in of themselves, the ethereal vocals and instrumentation are enough to make you tear up.