From The TV IV
A mystery is a genre of TV shows, particularly dramas, in which each episode involves a puzzle or riddle which must be solved by the hero or heroes, usually called a detective (although that may or may not be his or her job title, as well). The majority of mysteries are crime dramas, and in the majority of these, the mystery is a homicide in which the killer must be found, but there are notable exceptions. Most mysteries encourage the viewer to solve the mystery with the detective, but that is not always the case. For House, M.D., for instance, the viewer would have to have an advanced degree in medicine before even attempting to solve the mystery before the detective, Dr. Gregory House; and in Columbo, the murder was shown in the first act, which created a sense of dramatic irony as the audience knew who the killer was, but the detective, Lt. Frank Columbo, did not. Other notable mysteries throughout TV history include Dragnet, Magnum, P.I., Murder, She Wrote, Law & Order and CSI.
Mysteries can also be serialized in which the mystery is not solved in one episode but across a season or the entire run of the show or in which various mysteries are constantly introduced and solved across multiple episodes. The key to a serialized mystery is introducing enough clues to keep the viewer engaged but not so many that it becomes unbelievable that the characters have not solved it. Notable cases of serialized mystery shows include Twin Peaks, Lost, and Desperate Housewives.
Some shows also have a mix of episodic mysteries that are introduced and solved each episode and serialized mysteries that are solved over time. This is kind of a best of both worlds style since they have the pay-off of a newly solved mystery each episode and the long term draw of a serialized mystery. Some notable shows with a mix of serial and episodic mysteries are The X-Files and Veronica Mars.
See the Mystery category for a list of mystery shows.