According to About.com a mystery is:
Definition: Mystery is a genre of fiction in which a detective, either an amateur or a professional, solves a crime or a series of crimes. Because detective stories rely on logic, supernatural elements rarely come into play. The detective may be a private investigator, a policeman, an elderly widow, or a young girl, but he or she generally has nothing material to gain from solving the crime. Subgenres include the cozy and the hard-boiled detective story.
That seems pretty simple and straightforward, doesn't it? But it sure gives us a lot of latitude. My mystery can be a police procedure with accurate details in the day-to-day work of a police investigation -- kind of a CSI type mystery. Or a Women's Murder Club.
My mystery can be an unsuspecting young woman who has to figure out who killed her boss and why, before she's the next victim, although that does certainly give her a real something to gain, other than material gain! My detective can be a Miss Marple, Harry Bosch, Nancy Drew or Gil Grissom type. My mystery can be a murder, a robbery, a kidnapping or any other crime.
Your mystery can be whatever you like -- the kind of detective and crime you like to try to figure out. It can be whenever and wherever you want it to be. As a writer, you can write the mystery you love to read. As a reader, you can seek out the writers who write what you love to read.