The scene where Tod's owner has to abandon him in a game preserve for fear that the hunter will eventually kill him (he even threatens her with "You can't keep him locked up forever!").
The abandonment scene is made even worse by the fact that Tod has no concept of why she is doing it, and he tries to follow her. And the tearjerking song the woman sings about how she really doesn't want to do this.
The echo of one of the early lines played at the end:
Tod: Copper? You're my very best friend.
Copper: And you're mine too Tod.
Tod: And we'll always be friends, forever, won't we?
Copper: Yeah, forever!
The scene where Tod reunites with Copper, after the latter had spent the winter evolving into a prime hunting dog. After noting how big they've both grown, Copper says that Tod shouldn't have come.
Copper: It's great to see you again, Tod... but you shouldn't be over here. You're gonna get us both into a lot of trouble.
Tod: Hey, I just wanted to see you. We're...we're still friends, aren't we?
Copper: Tod... those days are over. I'm a hunting dog now.
Upon hearing this, Tod recoils in disbelief... then hangs his head and closes his eyes, crushed by the finality of Copper's statement. The crestfallen look on his face is just...heartbreaking.
The song "The Best Of Friends".
When Amos takes Chief and Copper on a hunting trip, Copper's initially excited and raring to go. But when he looks out from the car he can see Tod staring at him nearby and starts howling mournfully. Made even more tragic by the fact that it's the last time they see each other while they're young before Copper grows up to become a highly trained hunting dog.
The part at the very beginning when Tod's mother, running away from a hunter with the young kit in her mouth, sets Tod down by the fence and then gives him a couple licks— as if saying good-bye— before running for the hill and getting shot as soon as she's out of view.
There's also the moment when Todd and Copper face off in the climatic sequence, snarling with fangs bared and ready for battle. As much as it's a thrilling scene, it's also heartbreaking that two childhood friends have come to this.
The part where Copper defends a barely conscious Tod after his fall. From his own master no less. If that didn't push you to tears, the small whimper he gives to Amos will.
And just before that, when Copper finds Tod in the water. Tod's been on the run from Amos and Copper. He's fought Copper and wounded him several times. He dove through flames. He battled a bear that weighed a hundred times what he did, and won, just to save the friend who was trying to kill him. When he sees Copper, the look on his face is a very sad acceptance of the fact that he's completely out of fight and at Copper's mercy.
Lindsay: The worst thing about this one is that no matter where it ends, you are where you were in the original. In the middle of The Fox and The Hound: being torn apart by society. And that's horrible.
The gassing of Tod's first litter, and the mother's reaction:
The vixen was there. She had dug up the bodies of the cubs and laid them out in a row. Their coats were damp where she had licked and licked, trying to restore them to life. Beside the biggest pup was a fresh-killed chicken she had gotten from the barnyard, hoping the odor of his favorite quarry might bring him back to consciousness. All night she worked over them, and it was not until morning and the blowflies came that she would admit the tragic truth. Even then, for days afterward she returned to the den, hoping upon hope that a miracle had happened and that the cubs would once again run out to greet her.
Tod's first mate's horrible death in a leghold trap.
The ending. The ending. Tod - the Great Fox - is finally dead, killed in a last hunt by the hunter and Copper, the last of his hunting dogs. Copper's master has a surge of popularity, but soon after has to go to a nursing home where pets aren't allowed. The master is forced to shoot Copper to avoid abandoning him.
...and in this miserable, fouled land there was no longer any place for fox, hound, or human being.