After you kill the Enderdragon, you are treated to a conversation between two strange beings, who appear to be the true architects and creators of Minecraft. What they say, and what they say to you, is strangely heartwarming.
and the universe said I love you because you are love
With the new breeding feature, which let's you breed 2 animals to create a baby animal, it's heartwarming to see the adults surround the baby.
And some mods add more animals, and therefore more cute babies (and pets)!
The Iron Golems handing roses to Villager children is quite touching.
Wolves love you more than their own pack and their own lives after you tame them, they even let you injure them.
Playing in creative mode, and spawning hostile mobs that don't attack you (unless you attack them). You can walk (or fly) up to them and they'll be utterly passive towards you. Now it's possible to have pet creepers and more!