Random Encounters

In games like Fallout New Vegas a random encounter is a special event that occurs randomly, like having unqiue characters spawn and fight each other, or having someone approach you with a quest.
Alot of other games do this, Minecraft would be perfect for this sort of thing!

You could have an Enderman running away from a pillager with a block he stole from him.
A Mooshroom cow randomly walking across grass plains it normally wouldn't spawn in.
A villager getting attacked by phantoms that would reward you with loot if you killed them for him.
Dolphins fighting Drowned in the water.
Skeletons fighting Spiders.
Random villager that just stands around and fishes.
A scene of a traveling cart that had been ambushed by pillagers and have its barrels filled with loot which has fallen off close by.

Small things that just add to the experience without being too over the top or hard to implement.
A Random Encounter could be ANYTHING, it doesn't even have to have any mobs in it, imagination is the only limit!