In "That's My Mommy," Quacker confuses Tom as his mother, despite Tom's efforts to eat him. When Quacker realizes this (while preparing a recipe for "Mommy"), he looks forlorn and marches up a spoon leaning on the pot, preparing to cook himself ("Well, if my nice sweet mommy wants a duck dinner, my nice sweet mommy's gonna have a duck dinner!"). To really jerk the tears, Quacker says, "I still love you, Mommy!" just before he jumps into the water. It is at this point that Tom has a change of heart and saves Quacker from a boiling death. The two hug as tears stream down Tom's cheeks, and the cartoon ends with the two quacking at each other in a duck pond.
Tom really starts having a change of heart when Quacker tells Tom to take a break and let him cook. And it's solidified when Quacker tells him that he still loves him.
The endings of "The Night Before Christmas" and "Snowbody Loves Me" Basically the same thing—Tom makes Jerry stay out in the cold, but rescues him from freezing to death.
In "Puppy Tale", Tom kicks Jerry and a puppy Jerry had taken in out the house. During the night, a severe thunderstorm kicks up and Tom feels guilty for what he did, worrying that Jerry and the puppy could drown in the flood. He goes out to find them, only to be swept away by the flood waters. Jerry and the puppy (who were safe), find him and bring him back to care for him. When Tom wakes up, he then gives the puppy milk and the puppy calls all his friends to share with them. Tom (and Jerry) just looks on happily.
At the end of "Just Ducky," Jerry and the baby duck save Tom from drowning. Later on, when Tom comes down with a bad cold, Jerry wraps him in a blanket and feeds him soup, and the two wave good-bye to the ducks.
In "Hatch Up Your Troubles" and its remake "The Egg And Jerry", a woodpecker hatches and believes Jerry is its mother (because its egg rolled into Jerry's home). The bird irritates Jerry and he eventually kicks it out, but when Tom goes after it, Jerry saves it multiple times. Then, when its real mother comes to get it, it flies away with her, leaving Jerry sad until the woodpecker returns to give Jerry a kiss and Jerry then happily waves goodbye. Aww.
At the end of "Heavenly Puss", the moment Tom hugs and kisses a confused Jerry is just too sweet (and kind of funny).
Even before that, Jerry signs the Certificate of Forgiveness when he realizes what will happen to Tom if it isn't signed. He may not like Tom, but no one deserves Hell.
In the Chuck Jones cartoon "The A-Tom-Inable Snowman," when Tom catches a cold and is shivering/sneezing like mad, (or at least, pretending to,) Jerry sits close by, looking incredibly worried about the guy. Jerry even begins to hand him a tissue when he weakly gestures towards the tissue box; (that is, until Tom quickly recovers and grabs Jerry, preparing to eat him...)
In an odd example of an entire character being a Crowning Moment of Heartwarming, there's the Saint Bernard who repeatedly pops in and out of the cartoon to rescue Tom. Doesn't hurt that the dog's character design is irresistibly cute and dopey-looking.
Then there's "The Cat and the Mermouse", where Jerry saves Tom from drowning.
Tom's reaction to Jerry saving him- he looks at Jerry with sincere gratitude and gingerly shakes his hand.
In "Tom and Jerry Meet Sherlock Holmes", after Jerry is captured by the henchmen, Tom springs into action to save him.
In "Tom and Jerry Meet the Wizard of OZ", when Miss Gulch takes Toto away from Dorothy, Tom and Jerry were incredibly saddened by this and what do they do about it... they fixed a makeshift bike and went after Miss Gulch and managed to save Toto. Lesson learned from these movies... It's never a good idea to upset BOTH Tom and Jerry!
The ending of "Little School Mouse" is both hilarious and heartwarming — all through the cartoon, Jerry has been acting as a teacher to Nibbles (complete with blackboard and pointer) teaching and testing him in the ways of cat-outwitting. Nibbles has managed to pull off most of the tests, though generally (and to Jerry's increasing frustration) through kindly asking Tom to comply. The final test is to tie a bell around the cat's neck, which Nibbles solves by gift-wrapping the bell and giving it to Tom as a present. Tom loves the present, puts it around his neck and is thrilled with Nibbles's kindness. The final scene has Nibbles as the teacher, now teaching a grumpy Jerry and a smiling, enthusiastic Tom that cats and mice should be friends.
"Mouse In Manhattan". Jerry ditches Tom because he's bored of country life and heads to New York City. The end of the episode has Jerry running back to the relative safety of his old home, and kissing a confused Tom (who never read the goodbye note Jerry left).
The song between Robin Hood and Maid Marian in Robin Hood and His Merry Mouse.
The episode "The Truce Hurts" has Tom, Jerry, and Spike putting aside their differences to live together happily. Even if it's short-lived, they actually try to make the effort to protect each other, as Tom saves Jerry from becoming Butch's lunch, and Spike punches out a dog ready to eat Tom. It's actually pretty sweet seeing them get along, proving that, when motivated, they actually would be able to live together in harmony.
Neapolitan Mouse. Aside from a quick chase in the beginning, there are no chases, no plots, no elaborate schemes, nothing like that. It's just Tom and Jerry befriending a little Italian mouse, who is a huge fan of their cartoons, and enjoying the sights, smells and delicacies Italy has to offer. Tupo may have only appeared in that one episode, but he is very memorable for a very big reason.
The most heartwarming part of this short is arguably how Tupo defends first Jerry from Tom, and later Tom from a local bullying greyhound, with the reasoning that he hates it when someone thinks they can bully others just because they are bigger and stronger. Tupo posseses a degree of super strength and uses it to protect anyone who is victimized.
In "The Million Dollar Cat", Tom is able to inherit a million dollars on one condition: he doesn't hurt any other being. After a episode's worth of torture from Jerry abusing this handicap, Tom finally cracks and attacks Jerry. Though he initially laments "throwing away a million dollars", he happily goes back to attacking Jerry, not caring because his moral victory is worth more to him than the money.
At the end of both "Lonesome Mouse," and "Old Rocking Chair Tom," after Tom "rescues" Mamy from Jerry (who in both cases were really just plotting to let Tom back into the house,) Mamy rewards him by giving him a pie,and apologizes for throwing him out of the house. Harsh as she can often be, it's pretty clear that she values Tom greatly.
In the latter example, Tom shares his pie with Jerry.
Life With Tom is a Clip Show featuring previous Tom and Jerry cartoons written as the titular book. Tom is furious that the book has made him a laughingstock...but then Jerry revealed that he instructed the publishers of his novel to give half of his $50,000 royalties to Tom.
Simultaneously funny and heartwarming is how Tom then flips through the book again and finds it Actually Pretty Funny.
In Professor Tom, Jerry befriends a young kitten named Topsy. He teaches Topsy that cat and mice like them should be friends instead of enemies. They work, and after they defeat Tom, the two walk away as friends, holding hands.
Tom's girlfriend in Muscle Beach Tom. She's a beautiful and nice cat who is enjoying herself. She dances delightfully to the radio music and is filled with joy by weightlifting. It's no wonder Tom, Butch and Jerry all fall in love with her and fight to win her heart.