Paranoia was an overwhelming fear of one's environment and/or current situation, often leading to illogical responses to various stimuli, however minor.
Upon traveling back to the year 1986 with his senior staff, James T. Kirk cautioned them that the surrounding culture was extremely primitive and paranoid. (Star Trek IV: The Voyage Home)
In 2154, when Commander Thy'lek Shran suggested that a seemingly Andorian warship which had attacked the Enterprise NX-01 had been taken and reconfigured by Tellarites, the Tellarite ambassador, Gral accused him of paranoia. He replied that he was not paranoid, that the Tellarites were trying to kill his people. (ENT: "Babel One")
Kelpiens experienced hyper-vigilance and paranoia, especially pre-vahar'ai, as they had evolved to be able to flee predators and sense danger. (DIS: "The Vulcan Hello", "An Obol for Charon")
In 2365, a psychotronic stability examination Data showed the presence of a secondary, "sensitive yet paranoid" personality within the android; that of Dr. Ira Graves. (TNG: "The Schizoid Man")
When a humanoid is unable to enter into REM sleep for a prolonged period of time, they may suffer from paranoia or hallucinations. This happened to the crew of the USS Enterprise-D when it became trapped in a Tyken's Rift, in 2367. (TNG: "Night Terrors")
In 2369, Ferengi bartender Quark told Constable Odo that he thought he was paranoid, after Odo spotted two Miradorn nodding in his direction. Denying any suggestion that he was involved in illegal activities, Quark theorized that all shapeshifters must be the same, evidenced by the fact nobody had seen one at that point. (DS9: "Vortex")
Later that year, the IKS Toh'Kaht fell under the influence of a set of energy spheres on Saltah'na, causing paranoia and factionism among its crew, a re-enactment of the events that led to the destruction of the Saltah'na species. (DS9: "Dramatis Personae")
The Kesprytt were a species native to the planet Kesprytt III. They were divided into two rivaling countrys known as the Kes and the Prytt. In 2370, the bigger part of this species (the Kes) applied for associate Federation membership, but this request was denied. Due to the long conflict between the two nations, all Kesprytt had developed a strong sense of paranoia and xenophobia. (TNG: "Attached")
Also in that year, the replicant version of Chief Miles O'Brien described the Paradans as being paranoid due to their obsession with security, though he could understand it after twelve years of civil war. (DS9: "Whispers")
During one of their lunches on the replimat of Deep Space 9, in 2371, Doctor Julian Bashir called Garak paranoid after the Cardassian spy-turned-tailor implied that he would be killed should he leave the station. (DS9: "Second Skin")
Later that year, Garak used the term when referring to Gul Dukat's counter-insurgency program and the unusually large number of interrogative subroutines he had planted in the code. (DS9: "Civil Defense")
Also that year, an outbreak of paranoia happened on the USS Voyager when an unknown entity, which was actually the consciousness of Chakotay, began inhabiting the minds of various members of the crew, trying to protect them from the Komar. (VOY: "Cathexis")
In describing creative differences between him and Michael Piller regarding this story, Brannon Braga recalled, "Michael Piller wanted to make it a story about paranoia, which sounded good at the time, but it's hard to do a show about paranoia on a Starfleet vessel. People don't behave that way." (Cinefantastique, Vol. 27, No. 4/5, p. 63)
Unknown that she and Tom Paris were scanned by the Srivani, B'Elanna Torres thought someone was watching her kissing Paris in a Jefferies tube. She then laughed about herself and thought she went paranoid. (VOY: "Scientific Method")
In 2374 in the alternate timeline known as the "Year of Hell," Lieutenant Tom Paris stated to Commander Chakotay regarding Captain Annorax's belief that time had a personal grudge against him, "That's called paranoia, Chakotay, with a hint of megalomania." (VOY: "Year of Hell, Part II")
At the end of the year, Janeway hoped that she and Tuvok were "just suffering from some good old-fashioned paranoia" regarding their suspicions about Arturis and the USS Dauntless. (VOY: "Hope and Fear")
During the negotiations with Species 8472 in 2375, Captain Janeway called it a paranoid debate as the "Boothby" replicant spoke against every claim Janeway made. (VOY: "In the Flesh")
In 2376, Deputy Investigator Naroq of the Kesat described the Ba'Neth as a being "paranoid and xenophobic." (VOY: "Riddles")
In 2377, Chakotay urged the Voyager's Maquis crewmembers not to give way to paranoia after a number of them had fallen victim to an unknown assailant. (VOY: "Repression")
In 2399, Raffaela Musiker described her life following having been fired from Starfleet as having been a long slide into humiliation and rage with, admittedly, "a fair amount of snakeleaf-induced paranoia," noting that some things never changed. (PIC: "The End is the Beginning")