The mystery genre appeals to me mostly for the suspense element. I don't want to read or watch horror movies, as they terrify the hell out of me, causing sleepless nights and feeling as though the murderer is hiding behind the shower curtain, or in a closet!
While reflecting on suspenseful books, movies and stories I have experienced in my life, the movie "The Sixth Sense"comes to the forefront! The audience was captivated by the boy's relationship with his psychologist. It was apparent throughout the movie that the psychologist's wife was not happy about  her husband's relationship with the boy. She was quite bitchy toward her husband, and ignored him a lot. The boy could see dead people, and had conversations with them, which caused alarm for the boy's mother.
The audience was captivated by the suspense of the why the boy saw dead people, and would the award winning psychologist cure his problem. At the end of the movie, the boy was in a bed, I seem to remember he was hospitalized for his problem, but I could be mistaken on that fact. The boy was telling  his doctor that he talked to dead people, and they didn't even know they were dead. The scene changed to the doctor's wife who fell asleep watching their wedding video, as their anniversary had just come and gone. She shivered from the cold of being visited by a ghost, as she fell deeper into sleep her had relaxed and her husband's wedding ring fell from her hand and rolled across the floor. As this happens, the doctor looked down, and noticed he wasn't wearing his wedding ring, as it rolled across the floor, and realized HE WAS DEAD! The audience, myself included sat straight up and said, "Oh My God He's Dead!"
I realize it is a different take on the mystery genre, as no one is solving a crime, a good guy and a bad guy situation, or a a whodunnit. Yet, the suspense is what made it a mystery genre film for me. I was captivated by why the wife was so bitchy and ignored her husband, and in one scene, yelled at him. She knew she was being visited by her husband's ghost, yet he, and the audience didn't.
I may be off target for this assignment, I'm not sure. However, the question posed was why the mystery genre appeals to me, citing an example, and why it was special to me. For me, a mystery genre story involves the suspense element, it could be ghosts, or a murder mystery, or perhaps an art heist, yet the common denominator would be in place, suspense!