Defamation is the term used when a statement hurts a person's reputation.  If the defamation is spoken, it is called slander (written defamation is called libel). 

Although slander is it not a crime, it is a tort, meaning that one who has been slandered can sue the offending party for damages in civil court.  Defamation law tries to balance two opposing ideas.  One, that people should be allowed freedom of expression without fear of being sued.  Two, that people should not destroy other people's lives by telling lies and spreading rumors.  Generally, slander is not considered as serious as libel.

If you decide to sue someone for slander, generally you will need to prove four things:

1)  That the statement was actually made.

2)  That the statement was "published," meaning heard by a third party.

3)  That the statement was false.  Otherwise, it isn't considered damaging.  And if the statement is true, then it isn't considered slander.

4)  That the false statement caused some kind of injury to the person's reputation, meaning that they were ostracized by neighbors or lost their job, etc.

And some people have "privilege," meaning that they cannot be sued even if the statements they make are false.  These include witnesses in court and lawmakers.  In addition, public figures have less protection from slander claims than do private citizens.