Three is a magic number. If something is done or mentioned or experienced by characters once, you have an opportunity to repeat it two more times.
This could be three people murdered (or at least found dead) in a mystery, but it could also mean three banks get robbed. In other words, three crimes are committed.
This could mean the main character lands in a dangerous situation (or at least a fight) three times in an action-adventure tale. In this case, each situation should get the ante upped -- first time he ends up in a fist fight, second time he escapes more serious injury, third time he escapes getting killed.
A character who seems to be a minor one could appear three different times: first just seen in passing but in a way that catches the main character's attention, second time actual interaction between this character and the main one, and third time (depending on the genre) could be the charm or the near death experience.
The only down side of using the number 3 for elements like those noted here is that you can only use it for things involving the same character or characters in a single story once.
The good thing is that you can use the number 3 for other elements, like the way a chapter is broken down.