Elizabeth Short: "The Black Dahlia"A 22-year-old actress-in-waiting (i.e. unsigned) found nude, sodomized, and horribly disfigured in a field near Hollywood on January 15, 1947. Before her death, she had jet-black hair and a penchant for beautiful black dresses, and this led to her nickname "The Black Dahlia", which was trumped up by newspaper reporters at the time.
She has been linked romantically to Marilyn Monroe, but that sort of thing tends to happen after the fact; other sinister and conspiratorial reasons have also come to light, more likely to sell a story than anything else.
The murder was never solved, and a number of books have appeared to try and explain who did it. This isn't to say the murder is lacking for leads; many men and women have confessed to Short's murder but all have been found to be lying for whatever reason people do such things.