There are many different types of crimes and like the first responder suggested there are many ways of breaking them down. I will break them down by type.
Sex Crimes- sex crimes are crimes that revolve around a sex act or attempted sex act. Some examples are: rape, child molestation, child pornography, child prostitution, incest, and etc.
Homicide- is a crime that involves the killing of another person.
Child Abuse- is any kind of abuse aimed at a child. This can be sexual in nature, physical and emotional.
Kidnapping- is the taking of a person without their consent or that of their parent
Money Laundering-is any transaction that which generates an asset or a value as a result of an illegal act.
Below is a link to many other types of crimes.