A ghost story was a story that featured a ghost as the main plot element.
Travis Mayweather was known for telling ghost stories. (ENT: "Oasis")
In 2151, while spending shore leave around a campfire on a previously unexplored Minshara class planet, Mayweather told his shipmates from the Enterprise a tale supposedly told to him by his uncle about an escape pod floating in space for 63 years. George Webb, sent to investigate it, heard a tapping coming from inside, but upon opening the pod, found it to be empty. He later began acting strange, getting into fights with his crewmates and muttering in an alien language. Finally, he overloaded his vessel's impulse reactors then sealed himself in a life pod and ejected it. Some theorized that the alien lifeform got to him, others that it was the ghost of the dead crewman, though it was Mayweather's personal theory that Webb was still drifting in space and that the echo of his distress call can still be heard when subspace noise is low, a beeping noise. When T'Pol expressed skepticism at the idea of a distress beacon could continue to work after 63 years, Trip Tucker quipped, "Let me guess. No ghost stories on Vulcan." He later asked if anyone had heard the story about a haunted comet. (ENT: "Strange New World")
Later that year, while exploring a derelict Kantare supply ship, Travis doubted scavengers explained D'Marr's experience, as they would have stripped the ship of everything usable. Jonathan Archer then quipped, "This isn't turning into one of your famous ghost stories, is it?", to which Mayweather replied, "Would make a good one, sir." (ENT: "Oasis")
In 2152, Hoshi Sato claimed no knowledge of Cyrus Ramsey, saying that she must've fallen asleep on the survival overnights before hearing the ghost stories. (ENT: "Vanishing Point")
In 2267, while considering their frightening surroundings on Pyris VII, James T. Kirk mentioned ghost stories as an example of what Spock noted, that it was "As if someone knew what it was that terrifies man most on an instinctive level." (TOS: "Catspaw")
As a child, Beverly Crusher listened to ghost stories by the light of her grandmother's candle. (TNG: "Sub Rosa")
In 2367, upon hearing of Kenicki's supposed sighting of a disappearing turbolift passenger wearing an old Starfleet uniform from Gillespie, Miles O'Brien dismissed the tale as a ghost story. (TNG: "Night Terrors")