I'm surprised nobody has mentioned this yet. Maybe it's because there are a lot of people with very strong opinions on the topic, but the mystery that creeps me out most (right now - these are all great) would be the identity of Jack the Ripper.
We did a 'Jack the Ripper' tour in London recently (tacky, but intriguing), and to be honest before this point I'd never looked into the topic. What shocked me was the brutality and utter misogyny of the murders, and how they continued to become more base and defiled as he progressed. I wasn't previously aware that he was possibly a cannibal, with the police receiving a letter from someone claiming to have 'enjoyed' the kidney of one of his victims. Also, the suddenness with which they stopped.
There's always the possibility he got syphilis from a prostitute - it would explain a lot of things, like the hatred of 'working women', the insanity (because there is no other word to explain what he did to those peoples' bodies), why the attacks progressively became more risky and debased, and the sudden stop (people were often picked up and placed in asylums permanently). Tertiary syphilis is a nasty condition.
There is something particularly sinister about his crimes, and the sloppiness of past forensics (which was in its infancy at the time) means unfortunately we probably won't ever have an answer.
As always, more info: http://en.wikipedia.org/wiki/Jack_the_Ripper . I wouldn't recommend blowing up the photo of Mary Kelly, his final victim - it's pretty NSFL (gore, obviously).