Throughout the game, there are several random events that can occur. This is by no means an exhaustive list yet:
There is a random chance that a meteor can fall from the sky onto The Farm at random tiles during night. A unique sound effect will be heard before daily earnings. In the morning, a message will pop up saying "An explosion was heard in the night..."
The Crop Fairy
During random nights of the growing seasons, there is a chance for the Crop Fairy to appear after daily earnings. She will select an area that contains crops and transform them so they can be harvested. Everything from a 1x1, 4x6, to a 5x5 area has been reported. It has also been reported that she could revive crops after the end of their growing season when they are supposed to be dead.
She also seems to stop animal fodder from being eaten overnight, removing the need to refill it. She would fly over a silo and restore all the hay to the top. (Requires confirmation)
In a random event after you sleep, a witch will fly over your Farm.
The witch has also been reported to fly over the silo, but what it does is unknown.