There is no song that makes me cry everytime I hear it. Everything will lose it's potency on me after the first couple of times. But anyway a few of the songs that made me cry in order of just teary the first time to openly sobbing quite often

Tears in Heaven - Eric Clapton
Adam's Song - Blink 182
Last Kiss - Pearl Jam
Alone Again (Naturally) - Gilbert O'Sullivan
How Soon is Now - The Smiths
Mad World - Tears for Fears