Any moments between John in his pre-Jigsaw days and Jill are heartwarming enough, his video will and Jill's Gideon tape are stand outs. You could they loved each other very much and what followed more heart breaking for them.
Lawrence and Adam's last minutes together before the former left the bathroom, bleeding from his leg-stump and promising to get help for the two of them is something of a tender moment.
A deleted scene from the third film shows us a kinder, Adorkable side of Adam; apparently seeing Amanda beforehand in his apartment, he compliments her "rockstar hair", offers to take her to see his buddy's indie band, and even snaps a photo of her. She may not have been as energetic as he, but they still kind bonded~
Saw III: Seeing Eric Matthews put himself through enough pain to make a hardened police veteran cry, in order to escape a trap that was intended to kill him, all in the name of finding and rescuing his son, Daniel. The kicker was the visual of Matthews, feebly limping through the corridors, desperately shouting the name of his son.