Defining what is a crime can be a difficult task depending on the place it takes place. I mean that what is a crime in The United States, might not be in Japan, for example. In addition to that, there are some places that don't have written laws about what cases are considered crimes which make the task even harder.
An example of a situation in which a crime might not be considered criminal is when we see a couple having an argument and all of a sudden one of the parts is hanging the other, and the only option the other person have to survive is to grab a trophy and hit it to the head and the person dies. This can not be considered as a crime because the one that "murdered" the other acted in self-defense.
It is important to mention that a person can't be convicted for a crime if it was deemed an unpreventable accident, ignorance, self-defense or insanity.