Gepetto's Adult Fear scene when he walks the raining streets in search of his puppet-son who never returned home from school is hard to watch... Gepetto wanted this little puppet boy to be real so he could have someone to love and care for... and now that person isn't there...
Gepetto: [agonizingly] What could have happened to him? Where could he be at this hour? [determinedly]...I better go out again and look for him.
Geppetto walking through the pouring rain at night, his forlorn cry for his boy drowned out by a crack of thunder. He looks so helpless.
Also when Jiminy discovers the pen where the Coachmen keeps the donkeys that can still talk.
This line from Jiminy when he discovers this atrocity. He's abandoning Pinocchio and his duties as conscience, but when he see what the boys on Pleasure Island end up becoming, he rushes back to save Pinoke.
Jiminy: Boys? So that's what...PINOCCHIO!!! [later] I hope I'm not too late!
Lampwick's transformation. Especially the part where he begs Pinocchio for help, even telling him to call Jiminy not realizing that Jiminy, having learned of the island's curse, was already on his way but would not be there in time to save him.
Bit of Fridge Horror/Fridge Tear Jerker in it when you realize: those boys' parents will never know what happened to their sons. All they will ever know is that one day, their little boy didn't come home...
Lampwick crying for his mom. He may be a jerk, but still... poor kid.
"Pinocchio... Swim for shore! Swim for shore! Save... yourself..."
May not be a common thing for audiences nowadays but apparently Pinocchio's apparent death scene contributed handsomely to the well of tears Disney seeks to reap from its audiences.
"When You Wish Upon A Star". So happy that it brings tears.