"When She Loved Me" will often make me a complete mess. It didn't always do this, though...you see, I listened to it one night just a few days after my dog of 11+ years died, and all I could think about was how I had grown up (I was 5 when I got her, 16 when she died) and stopped paying so much attention to her...
I stayed the same--but she began to drift away, I was left alone
Still I waited for the day, when she'd say 'I will always love you'
...which is exactly what I said to her at the vet before we put her down. I felt like I was Emily, and she was Jessie. You can see where the waterworks come from. That was over two years ago, and that song still makes me extremely sad sometimes.
I sometimes cry during "Two Worlds" from Tarzan, when Kala's baby is eaten by the cheetah. I also cry during Wishes, but only when I see it at the parks.
Honestly, if I'm in the right mood, many Disney songs can make me cry! But that TS2 one is the worst.