Aspect of Fairy Tales - Sets of 3

Sets of 3 can occur to prove that something is not just due to coincidence without becoming too monotonous, as if something occurred just once or twice it could be chance.

3 is also a number often used in history, such as the ancient Greeks and Romans had 3 graces.

It can also be associated with magic, for example in Shakespeare's Macbeth there where 3 witches. 

3 is also a spiritual angle - there are 3 states of craftsman; apprentice, journeyman and master, 3 states of matter; solid, liquid and gas, 3 tenses of time; past, present and future etc.

It may also have biblical connotations, referring to the Passion of Christ in which there is a 3 day interval between Good Friday and Easter Sunday.