A crime in a non-technical sense, is an act that violates a political or moral rule. But in many nations, the governments have discovered that informal sanctions are ineffective to control some types of antisocial behavior, so the system of social control has to be formalized. 

So crime can be construed as

1. An action prohibited by law

2. A failure to act as required by law

3. An activity that involves breaking the law

4. Any act considered morally wrong or shameful

5. An unwise, or regrettable act