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.
In a random event after you sleep, a witch will fly over your Farm.