According to The List Universe:

1. The Shroud of Turin:

The shroud of Turin is a linen cloth bearing the image of a man who had apparently died of crucifixion. Most Catholics consider it to be the burial shroud of Jesus Christ. It is currently held in the Cathedral of St John the Baptist in Turin, Italy. Despite many scientific investigations, no one has yet been able to explain how the image has been imprinted on the shroud and despite many attempts, no one has managed to replicate it.

2. Mary Celeste:

On November 7, 1872 the ship departed New York with Captain Briggs, his wife, young daughter and a crew of eight. The ship was loaded with 1700 barrels of raw American alcohol bound for Genoa, Italy. The captain, his family and crew were never seen again. The ship was found floating in the middle of the Strait of Gibraltar. There were no signs of struggle on board and all documents except the captain’s log were missing.

3. The Taos Hum:

The ‘Taos Hum’ is a low-pitched sound heard in numerous places worldwide, especially in the USA, UK, and northern europe. It is usually heard only in quiet environments, and is often described as sounding like a distant diesel engine. Since it has proven indetectable by microphones or VLF antennae, its source and nature is still a mystery.

Dang! I’ve heard this. I thought it was just me!

4. The Black Dahlia:

In 1947 the body of 22 year old Elizabeth Short was found in two pieces in a parking lot in Los Angeles. According to newspaper reports shortly after the murder, Short received the nickname “Black Dahlia” at a Long Beach drugstore in the summer of 1946, as a play on the then-current movie The Blue Dahlia. However, Los Angeles County district attorney investigators’ reports state the nickname was invented by newspaper reporters covering the murder. In either case, Short was not generally known as the “Black Dahlia” during her lifetime.

Many rumours and tales have spread about the Black Dahlia, and the investigation (one of the largest in LA history) never found the killer.

5. Comte de Saint Germain:

The Count of St. Germain (allegedly died February 27, 1784) was a courtier, adventurer, inventor, amateur scientist, violinist, amateur composer, and a mysterious gentleman; he also displayed some skills with the practice of alchemy. He was known as ‘Der Wundermann’ — ‘The Wonderman’. He was a man whose origin was unknown and who disappeared without leaving a trace.

6. The Voynich Manuscript:

The Voynich Manuscript is a medieval document written in an unknown script and in an unknown language. For over one hundred years people have tried to break the code to not avail. The overall impression given by the surviving leaves of the manuscript suggests that it was meant to serve as a pharmacopoeia or to address topics in medieval or early modern medicine. However, the puzzling details of illustrations have fueled many theories about the book’s origins, the contents of its text, and the purpose for which it was intended.

7. Jack The Ripper:

In the later half of 1888, London was terrorrised by a series of murders in the east end (largely in the Whitechapel area). The name Jack the Ripper was taken from a letter sent to a newspaper at the time by someone claiming to be the killer. The victims were typically prostitutes who had their throats cut and bodies mutilated. In some cases the bodies were discovered just minutes after the ripper had left the scene.The police at the time had many suspects but could never find sufficient evidence to convict anyone. In modern times there has even been some speculation that Prince Albert Victor was the murderer. Even with modern police methods, no further light has been shed on the murders in recent times. To this day no one knows who the ripper was.

8. The Burmuda Triangle:

The Bermuda triangle is an area of water in the North Atlantic Ocean in which a large number of planes and boats have gone missing in mysterious circumstances. Over the years many explanations have been put forward for the disappearances, including bad weather, alien abductions, time warps, and suspension of the laws of physics.

Although substantial documentation exists to show that many of the reports have been exaggerated, there is still no explanation for the unusually large number of disappearances in the area.

9. The Zodiac Killer:

The Zodiac killer was active in Northern California for ten months in the late 1960s. He killed at least five people, and injured two. He comitted the first two murders with a pistol, just inside the Benecia border. In his second shooting in Vallejo, he attempted to kill two people, but one survived despite gunshots to the head and neck. 40 minutes later the police recieved an anonymous phone call from a man claiming to be their killer and admitting to the murders of the previous two victims. One month three letters were sent to Newspapers in California containing a cypher that the killer claimed would give them his name.

10. The Babushka Lady:

During the analysis of the film footage of the assasination of John F. Kennedy in 1963, a mysterious woman was spotted. She was wearing a brown overcoat and a scarf on her head (the scarf is the reason for her name as she wore it in a similar style to Russian grandmothers – also called babushkas). The woman appeared to be holding something in front of her face which is believed to be a camera. She appears in many photos of the scene. Even after the shooting when most people had fled the area, she remained in place and continued to film. Shortly after she is seen moving away to the East up Elm Street. The FBI publically requested that the woman come forward and give them the footage she shot but she never did.

To this day, no one knows who the Babushka Woman is or what she was doing there.

Notably missing from the list are:

The Lindberg baby kidnapping, and

Amelia Earhart