Mama Bear Nadia using the last of her strength to push her baby towards Manny. Who uses his trunk to help her.
The entirety of the Original film.
Ice Age: The Meltdown
There's a flashback where Ellie the mammoth is orphaned in a snowstorm. She's alone and distraught until an opossum with two babies acknowledges her with only the kindest of smiles and decides to raise her as one of the family.
After Sid inadvertently helps save the day, the sloths that worshiped him and tried to sacrifice him want him to stay. Diego says that they need him more and says that he is what holds them together. Sid hugs the sabertooth tiger with joy with the sloths hugging one another when the others come to see.
Ice Age: Dawn of the Dinosaurs
when Manny and Ellie's daughter Peaches, was born.
Buck being accepted into the herd after Rudy dies. But it turns out Rudy had survived so Buck returns to the valley, but not before he and Diego bid farewell to each other.
The rest of the group pursuing Sid into the land of the dinosaurs, especially considering that Diego is set to leave the herd entirely immediately before. In a similar vein, Diego's first response to Buck's "Sid beat the dinosaur with broccoli" theory being that Sid isn't violent, only adding that Sid also isn't physically capable a moment later, was sweet.
The relationship between Manny and Ellie as a whole. Shows they've come a long way since the previous film.
Ice Age: Continental Drift
Manny's interaction with the paralyzed Sid.
At the end, Manny admits to Sid that he is not a screw-up, but a hero.
Also, Granny telling Sid that he has a real family: his friends.
Manny and Diego's interactions with Sid in the 4th one are in general a lot less vitriolic than in the first three movies. Possibly out of sympathy after his family abandoned him for the second time.