The Hopkinsville Goblin Case

In 1955, members of the Sutton family were out on their porch enjoying a relaxing visit/drinking binge with their good friend Billy Ray Taylor. Billy Ray decided to go out and get a drink of water from the well, when shit started getting weird.
He ran back in to tell everyone he'd seen some bright lights in the sky and that everyone should come look. According to one member of the Sutton clan, upon stepping outside the Suttons-plus-one encountered:
"... a luminous, three-and-a-half-foot-tall being with an oversized head, big, floppy, pointed ears, glowing eyes, and hands with talons at their ends. The figure, either made of or simply dressed in silvery metal, had its hands raised."

After seeing these figures coming out of the woods, showing the universal sign of surrender, the Suttons did the only thing they could do: try to kill their asses.

As they shot at the defenseless creatures with rifles, they claim to have heard clangs and ricochets as if the aliens were wearing some kind of metal armor. They said the aliens "flipped over and fled into the darkness when shot at.

The Lost Roanoke Colony

The Roanoke Colony was either the first permanent settlement in America, or an elaborate practical joke. Walter Raleigh sent the colonists there and then left them without supplies for three years, perhaps just to see what would happen.
What he probably didn't expect was for the colony to just vanish. When new settlers finally arrived, none of the original colony remained at the settlement (except for the old skeleton of one guy) and the mysterious word "Croatan" was carved into a tree, right under, "Metallica Rules".

So, was it a UFO abduction? Perhaps the colonists were held in some kind of suspended animation and are still being anally probed to this very day.

The Dyatlov Pass Incident

On February 2nd, 1959, during the cold winter on Kholat Syakhl ("Mountain of the Dead") in Russia, nine intrepid ski hikers decided to do what they do best, which is ski hike, whatever the hell that is. On February 26th, the first of their very dead bodies turned up. Man, who would have thought such a tragedy could strike on "The Mountain of the Dead?"

But it was the discovery of the campgrounds that added the icing to the creepy-as-fuck cake. The ski hikers' tent was shredded. The skiers were scattered around the grounds wearing either very sparse clothing or just their underwear. Three of them were found with crushed ribs and fractured skulls, but no visible defense marks or other signs of a struggle.

Oh yeah, and one of the bodies was missing a tongue.
In case you weren't already on the phone with Mulder and Scully, trace levels of radiation were supposedly found on their bodies. The official statement on what happened was about as vague and ass-covering as possible, saying it was caused by an "unknown compelling force." In laymen's terms this means, "fuck if we know."
The story has become an internet sensation over the years, with many people blaming aliens, and then ghosts, and then the yeti, or possibly all of them working in tandem.