Tamla Horsford

Initial reports were she died after a drunken fall from a balcony, but subsequent investigation found other indications that it might have been a murder that was covered up.

Mary Reeser

Spontaneous Combustion?

Overtoun Bridge

Reports of dog suicides
WHY?

Alcatraz

The famous escape from Alcatraz

Didn't the Mythbusters do this already? ;)

Lizzie Borden

Lizzie Borden took an axe
and gave her mother forty whacks.
When she saw what she had done,
she gave her father forty-one.

Amelia Earhart

Every few years someone finds some bit of circumstantial evidence

JonBenet Ramsey

This little girl was a 6 year old beauty pageant contestant. She'd been bludgeoned and then strangled to death.

Despite almost all the evidence pointing to the family, they were never charged. In 2008 the investigators formally cleared the family based on some DNA evidence.

DNA evidence is not the slam dunk everyone seems to think.

 

It's just a piece of the investigation puzzle, like any other piece of evidence, like fingerprints, weapons, footprints, etc.

But for some reason, most likely the way TV shows and movies have portrayed it, most Americans think it is the be-all, end-all of investigation.

 

(Fingerprints and hair analysis were treated like that when they first came out, as well.)

Atlantis

Atlantis was a fictional location made up whole cloth by the philosopher Plato. It was an allegory created just so Plato could talk about his philosophical principles using a fake location - much like Pan-Em in Hunger Games or Wakanda in the Marvel Comics.

This doesn't really count as a mystery, so proceed with caution.

Space Roar

Scientists studying cosmic background radiation detected a huge radio signal that they believe could possibly be evidence of the Big Bang

Somerton Man

Obscure "code" left behind along with Arabic verb for "is finished"

Cicada 3301

Alleged coding/cyberphreak organization that used puzzles to recruit members in the early 2010s

Gardner Museum Heist

Robert Gentile, the last mobster implicated, just died.

Roanoke

Croatoan

JFK

The official story is still questioned by a lot of people.

(Not me though. I've read the full Warren report and believe it to be an accurate representation of what happened.)