"Here's to insubordination."
- -Reginald Barclay, after acting insubordinately to holographic versions of Geordi La Forge and William T. Riker.
Insubordination was the act of a subordinate member of an organization willfully refusing to obey an order from their superior. Organizations with a chain of command, such as military forces, have insubordination as an offense to ensure that subordinates follow their given instructions. Officers who commit this act may face a number of penalties, such as being placed on report, transferred, or possibly stronger penalties such as being demoted or dismissed from service in the case of repeated offenses.
In either 2151 or 2152, Captain Jonathan Archer threatened to throw Commander Charles Tucker III in the brig of Enterprise NX-01 for insubordination if he revealed to a group of marauding aliens the location of the ship's vault containing bars of gold, though all of this was a ruse to trick the Ferengi, as there was actually no vault. (ENT: "Acquisition")
In 2154, after Sub-Commander T'Pol refused an order to complete an antimatter transfer, Captain Jonathan Archer stated that she could still be charged with insubordination, even though she wasn't wearing a Starfleet uniform. When she replied that they should perhaps contact Admiral Maxwell Forrest to discuss his recent behavior, he relieved her of duty as first officer and had her confined to quarters. (ENT: "Hatchery")
In 2286, Admiral James T. Kirk was convicted of insubordination by the Federation Council, specifically for disobeying Starfleet's directive prohibiting travel to the planet Genesis. The Council sentenced Kirk to a permanent reduction to the rank of Captain, and re-assigned him as Commanding Officer of the USS Enterprise-A. (Star Trek II: The Wrath of Khan; Star Trek IV: The Voyage Home)
In 2366, Lieutenant Reginald Barclay displayed insubordinate behavior toward holographic versions of both Geordi La Forge and William T. Riker. In the real world, Barclay was not openly insubordinate, but was frequently placed on report for infractions such as showing up late for duty shifts and displaying poor performance. (TNG: "Hollow Pursuits")
That same year, Ensign D'Amato was placed on report for insubordination towards Lieutenant Worf, his superior officer. Such behavior was surprising, as D'Amato had a history of being an excellent officer. It was unknown at the time that his behavior was due to the telepathy of Sarek, who was suffering from Bendii Syndrome and unknowingly projecting his emotions upon others. (TNG: "Sarek")
In 2370, Jean-Luc Picard, posing as a smuggler named Galen, described a captured William T. Riker as a Starfleet officer with a history of insubordination. Picard claimed that one instance of such behavior resulted in Riker being relieved of duty at Minos Korva. (TNG: "Gambit, Part I")
While searching for the USS Pegasus Jean-Luc Picard told Erik Pressman that, if Asteroid gamma 601 proved too dangerous, he would abort the mission. Furthermore, he informed Pressman that he was willing to face a court martial for insubordination. (TNG: "The Pegasus")
Beginning sometime in 2372, Lieutenant Tom Paris began displaying willful and insubordinate behavior, such as uncaringly showing up late for duty shifts, skimming profits from a gambling operation and talking back to commanding officers, particularly Commander Chakotay. It was later revealed, however, that this behavior was part of a cover to make it seem reasonable that Paris would want to leave USS Voyager, which itself was part of a greater plot to flush out a spy. (VOY: "Investigations")