For the same reason we have made shows such as Forensic Files, CSI, Law and Order, and the likes some of the most watched television ever.  We all LOVE solving problems and bringing closure to situations. It is the way our brain works by nature. When we are presented a situation that seems easy to figure out and then all of a sudden u start getting hints of something obscure luring about, we JUMP to it and we try to use our intelligence tools to crack the mystery. It is a natural curiosity and its fun!

Mysteries and detective fiction enable readers to both be in and out of a story.  The most famous, of course, are the Sherlock Holmes mysteries, which Michael Chabon says are the essence of literary criticism.

Chabon has written extensively on Holmes, namely the chapter from his new non-fiction collection of essays, Maps and Legends, in the chapter called, "Fan Fictions."  He says:

And yet there is a degree to which, just as all criticism is in essence Sherlockian, all literature, highbrow or low, from the Aeneid onward, is fan fiction. That is why Harold Bloom's notion of the anxiety of influence has always rung so hollow to me. Through parody and pastiche, allusion and homage, retelling and reimagining the stories that were told before us and that we have come of age loving—amateurs—we proceed, seeking out the blank places in the map that our favorite writers, in their greatness and negligence, have left for us, hoping to pass on to our own readers—should we be lucky enough to find any—some of the pleasure that we ourselves have taken in the stuff we love: to get in on the game. All novels are sequels; influence is bliss.

I think one reason people enjoy mysteries is that people like trying to figure out the answer to a puzzle. A mystery draws you in and keeps you hanging until the end. It is hard to put it down because you want to know how the story ends. In contrast, some other genres have more predictable endings (such as in a romance novel usually the hero and heroine fall in love and live happily every after).  In other forms of fiction, you form a rapport with the characters more fully - it is their lives and the situations in which they live that are important. In a mystery, the characters are secondary to the driving force of the plot - the over-riding question of "who done it?" that keeps us reading from cover to cover.

It is stimulating to try and pick up on the clues the author leaves behind for us to follow.  Reading a mystery, you know that there is a puzzle to be solved and that there will be twist/turns along the way.

With a non-mystery fiction, I tend to try and identify with the characters rather than examine them.  I don't usually question their motives unless the main character does.  Essentially, I get caught up in the story, but with the mystery I am trying to outsmart the characters.

While they are an escape from reality, mysteries are, in a sense, are a simulated reality that the reader can control.  When the reader solves a mystery, he/she may feel a renewed sense of esteeem and confidence that he/she may not have had in his/her life where things are beyond one's control.

I agree with the concensus. Most readers are more engaged in reading if they are actively involved and questioning the text. Mystery novels make this much easier than let’s say--books on education reform. Also mysteries are a means of escape from the reality of our lives whereas other types of novels might not be as much.

A good mystery will keep the reader on his mental toes throughout the story. Mysteries tend to get the reader more involved with the storyline as well as attempting to solve the problems at hand. A good, surprise ending is often a necessity, leaving the reader more satisfied when the story finally comes to an end.

What readers enjoy about a mystery is the intellectual challenge. A mystery often presents a problem, (most specifically a crime or a specific ill against a character or community) at the beginning and then offers clues that the reader can put together in order to hypothesize about a resolution. If it is in the form of a chapter novel, the end of each chapter usually includes a cliff-hanger.

If you take a look at some of the current mysteries on television, like the series 24 for example, people want to come back to watch the next week because a dramatic complication happens at the end of the current week's episode.

Take a look at enotes.com's criticism provided below to further understand.