The beginning where Pussyfoot isn't scared of him at all when he tries terrorizing him. He tries some more, but he just climbs up onto his back, kneads his fur, and then settles down. Becomes cute when he warms up to the kitten and kisses it on the forehead as he naps, and he licks him.
In "Scalp Trouble/Slightly Daffy" (the latter is a color remake of the former), Porky's a soldier at a fort, and Daffy's the general. Of course, Daffy's incredibly bossy and yells at the soldiers when they won't get up, and then he and Porky engage in typical hijinks trying to get out the door. On the way out, Daffy slips, and Porky catches him, bridal-style; Daffy bats his eyelashes at Porky, says, "Awwww, I didn't think you cared," and nuzzles his head against Porky's chin while Porky hugs him, laughing adorably. The fact that Porky and Daffy spend ninety percent of their cartoons trying to annoy and/or kill each other only serves to heighten the extreme levels of cute.
This wouldn't have seemed so heartwarming if it wasn't the Daffy Duck that deserved his name, and when he was just starting out.
Later on a similar short called "Father of the Bird" was made, again starring Sylvester. In that one he steals a bird egg, but he doesn't have the heart to eat the little bird when it hatches because it calls him "Mama." Begrudgingly he lets it go, but it continues to follow him, and soon Sylvester's going out of his way to rescue it from all the danger it puts itself in.
I think a lot of the cartoons with Sam Sheepdog and Ralph Wolf count. They're locked in a perpetual fight for the sheep, but at the end of the day, they punch their clocks and leave together as the best of friends.
Any time Pepe and Penelope are shown to have mutual affection for each other is touching, sadly such scenes usually don't last very long.
"Scaredy Cat" is mostly just nightmarish, but it does have one very sweet moment when Sylvester flees from the mouse-haunted house, leaving his owner Porky to be executed by the creepy mice. Sylvester's conscience appears to him and accuses him of being a coward, showing Sylvester a poster of him as a kitten being fed milk by Porky with the word "REMEMBER" over it. This memory stirs Sylvester to charge back into the house and rout out the mice in a rare victory for the Puddy Tat.
Really just the fact that despite how terrified he is, Sylvester still does everything in his power to protect his owner from harm in these shorts.
While the De Patie Freleng short "Fiesta Fiasco" is hardly among the gems of the series, it must mean something that Speedy went out of his way to organize a surprise birthday party for DaffyDuck. Extra points for actually being made during 1967; Daffy's 30th birthday.
Another case in the similarly questionable Cross OverPorky And Daffy Meet The Groovie Ghoulies. Daffy's iconically unpopular in the showbiz front. Frank however, loves him to bits.
At the end of Bah Humduck!, when Daffy almost reconsiders his newly-changed attitude.... Only for Porky's daughter to offer him a cookie, making Daffy decide to continue being generous.
A real-life example, which can also double as a Tearjerker: In his later years, Mel Blanc would often volunteer at children's hospitals, talking to sick kids in the voices of their favorite Looney Tunes characters.
At the end of 1963's "Woolen Under Where", Ralph is all set to blast Sam to kingdom come, but the clock whistles to indicate the end of their shifts. Sam and Ralph head home for the day, with Sam good-naturedly telling Ralph, "Better luck next time." As the two walk into the sunset, Sam says, "Good to be alive." Awww. Interestingly, this ending also counts as a Heartwarming in Hindsight if you realize that Mel Blanc, who voiced both of these characters and many, many others, almost died in a car accident in 1961. So the ending line could almost be seen as a Reality Subtext of Blanc pulling through and continuing to voice these famous characters. Good to be alive, indeed.
The ending of "Nelly's Folly" - Nelly has lost her fame and fortune due to having an affair with a married giraffe, and her lover wants nothing to do with her. Back in Africa, she's sadly singing to her animal friends (every single one of whom is in tears), when another male giraffe starts singing along with her, leading to Love at First Sight.
The ending of "Go Fly a Kit", where the flying cat and the female cat he saved reunite every spring. As the two sweetly stare into each others' eyes, their kittens come into view.