The crime of conspiracy is the act of collaborating with other persons to advance another criminal activity.
In 2286, the crew of the USS Enterprise, led by Kirk, was charged with conspiracy after their retrieval of Captain Spock from the Genesis Planet. The conspiracy, as charged, led to acts of assault, sabotage, theft, and destruction of Federation property. All of the charges except for one were summarily dismissed by the President of the Federation. (Star Trek IV: The Voyage Home)
In 2364, a race of neural parasites infiltrated Starfleet Command. Admiral Gregory Quinn was the first to suspect a conspiracy was going on at the highest levels of Starfleet. The alien plot was foiled by the efforts of the crew of the USS Enterprise-D and Admiral Norah Satie, among others. (TNG: "Coming of Age", "Conspiracy", "The Drumhead")
In 2369 the senior staff of Deep Space 9 talked about a way to arrest the Bajoran Kohn-Ma terrorist Tahna Los. Doctor Julian Bashir proposed that they could charge him of conspiracy and Constable Odo told that conspiracy is a crime. (DS9: "Past Prologue")
The same year, Commander Sisko was able to prevent an assassination attempt on Vedek Bareil Antos. When he talked with Major Kira Nerys after this incident and the interrogation of the assassin Neela, both believed they couldn't prove any connection to Vedek Winn Adami and Neela was the only one who was accused of conspiracy. (DS9: "In the Hands of the Prophets")
In 2377 Kadan conspired with the Quarren Ministry of Health and officials from Quarren Criminal Investigations to abduct aliens to relieve a massive labor shortage. This also included altering their memories so the victims would not realize their situation, and actually be happy to be working on Quarra. USS Voyager personnel were victims of this conspiracy, as well as numerous others. After being discovered, the Quarren ambassador promised that all the victims would be freed. (VOY: "Workforce", "Workforce, Part II")