I don't know if they literally make me cry, but they are very emotive:
Peter Gabriel: The Drop; Here Comes the Flood (1990); Mercy Street
Pink Floyd: Jugband Blues (It sounds like a Syd farewell); High Hopes; Shine On You Crazy Diamond
Elbow: Newborn
King Crimson: One Time
Ozzy Osbourne: See You on the Other Side
Paul McCartney: Here Today; Maybe I'm Amazed
The Cure: The Same Deep Water as You; Bloodflowers; Treasure; Going Nowhere; Apart; Trust; To Wish Impossible Things
Queen: The Show Must Go On
The Cars: Drive
Radiohead: How to Disappear Completely; Street Spirit (Fade Out); Paranoid Android; Pyramid Song
U.N.K.L.E & Thom Yorke: Rabbit in Your Headlights
George Harrison: Someplace Else


