(covers information from several alternate timelines)
The command chair, also referred to as the captain's chair or simply the chair, was the most important position on board a starship bridge. This seat, as its alternate name implies, was occupied by the captain of the vessel, or the officer who commanded the vessel in the captain's absence. The ship's duty officer sat on the command chair at all times and monitored all operations on the bridge. The chair was usually equipped with companels and other related equipment. In addition, some versions could swivel, so the commanding officer could easily turn to face any relevant station.
The right arm of the command chair on the bridge of the NX-class Enterprise NX-01 included a control panel that could flip up at the touch of a control. Additionally, both arms of the chair included at least one companel. An adjustable panel built into the chair's left arm had the additional capacity of being able to fire spatial torpedoes from the starship. (ENT: "Fight or Flight", "Cold Front")
While serving aboard Enterprise in May 2151, Vulcan Sub-Commander T'Pol used a companel on the chair's right arm to contact an away team on board an Axanar starship, and also contacted the armory by using a companel on the chair's left arm. T'Pol later deployed the docking arm by remotely extending it from the chair's right arm. (ENT: "Fight or Flight")
When Ensign Travis Mayweather assumed temporary command of Enterprise later that year, he was slightly hesitant to accept advice, from Ensign Hoshi Sato, that he occupy the command chair rather than his typical position at the helm. Once he moved to the captain's chair, Mayweather remarked, "The bridge looks a lot different from here." (ENT: "Cold Front")
In 2152, while passing a trinary star system that was emitting a dangerous form of radiation, the entire crew of Enterprise – with the exception of T'Pol – became affected and began to obsess over trivial matters. Charles "Trip" Tucker, the starship's chief engineer, became obsessed with the command chair which, according to Captain Jonathan Archer, was not comfortable enough. Commander Tucker eventually fixed the problem by lowering the chair one centimeter. (ENT: "Singularity")
In September of that year, a makeshift command chair, a cargo container with netting, was set up in a temporary command area for the crew's evacuation to Enterprise's catwalk. When Captain Archer first entered the command post, Tucker asked him if he wanted to try the chair out, though Archer replied, "Maybe later." (ENT: " The Catwalk")
In 2154, Captain Hernandez showed Captain Archer the bridge of her ship, the second NX-class starship, Columbia. Archer suggested the installation of a lumbar support in Columbia's command chair, as Hernandez would probably be spending a lot of time in the chair. (ENT: "Home")
When Enterprise was refitted following the Xindi mission, one of the additions was a completely redesigned captain's chair, which Commander Tucker joked "came with everything but its own protein resequencer." (ENT: "Borderland")
The command chairs installed aboard ships of the Constitution-class in the 2260s featured three slightly different versions of the same command chair. Most, such as the one on the USS Enterprise, featured a backrest that only reached the mid-back. The 2250s and 2260s version of this chair had a "gooseneck viewer" on the right armrest. (TOS: "The Cage", "Where No Man Has Gone Before") A few, such as that of the USS Lexington, had a full backrest. (TOS: "The Ultimate Computer")
During the early 2270s, Constitution-class starships went through a refit. The command chair of Captain James T. Kirk was upgraded with not only a full back support, including an automatically adjustable headrest, but also a safety restraint mechanism that allowed the armrests to hold down the occupant during turbulence and red alert. (Star Trek: The Motion Picture)
Upon Kirk stealing the Enterprise from Earth Spacedock for a self-appointed mission in 2285, Captain Lawrence H. Styles threatened Kirk that, if he went ahead with the theft, he would "never sit in the captain's chair again." This turned out to be partly true, as the Enterprise was self-destructed in close proximity to the Genesis Planet during Kirk's same unofficial mission, though Kirk did later assume the captain's chair of the Constitution-class USS Enterprise as well as a couple of other vessels (namely, a Klingon Bird-of-Prey named the HMS Bounty and, very briefly, the Excelsior-class USS Enterprise-B). (Star Trek III: The Search for Spock, Star Trek IV: The Voyage Home; Star Trek Generations) However, Kirk also admitted, while in command of the Enterprise-A in 2287, that he missed his former chair. (Star Trek V: The Final Frontier)
Alternate Constitution class
In the alternate reality, the Constitution-class command chair could swivel and was equipped with an intercom. (Star Trek) The chair also had self-extending twin-shoulder seat belts, as did other seats on the ship. (Star Trek Into Darkness)
Captain Christopher Pike was in the command chair of the USS Enterprise when the ship launched from Starbase 1 on a mission to Vulcan in 2258. Spock, as acting captain during Pike's absence, then occasionally occupied the chair, temporarily leaving it to go on a mission to rescue members of the Vulcan High Council including his mother, Amanda Grayson. After Spock returned, James T. Kirk momentarily assumed the chair. However, Spock told him to get "out of the chair", an instruction Kirk complied with. Once Kirk proved Spock was too emotionally compromised by the recent destruction of Vulcan to continue in command, the right to take the command chair became Kirk's. As Sulu informed the bridge crew of the fact that Kirk was now acting captain, Kirk quickly familiarized himself with the chair's controls and then used the intercom system to broadcast a message ship-wide that he was now in command and they were going to follow Nero to Earth. (Star Trek)
The next year, after Kirk violated Starfleet regulations by revealing the Enterprise to a group of primitive Nibirans, Christopher Pike accused Kirk of not respecting "the chair" because Pike felt Kirk wasn't yet ready for it. The Enterprise's command chair had never been occupied by Hikaru Sulu until Kirk temporarily promoted him to the position of acting captain, while Kirk led a landing party to Qo'noS and captured Khan Noonien Singh there. Later, Kirk, recruiting Khan to help him commandeer the USS Vengeance, promoted Spock to acting captain of the Enterprise with the rationale that the person who sat in the chair needed to know what they were doing. Moments after the power grids aboard the Enterprise started failing and the ship became caught in Earth's gravity, Spock activated the chair's seat belt. Shortly before the Enterprise commenced an historic five-year mission, Kirk assumed command and the associated chair from Sulu, who admitted he had enjoyed sitting in it. (Star Trek Into Darkness)
A few years later, Kirk once again used the chair's intercom to explain to the crew the nature of their mission when they were ordered to locate and rescue survivors from the other side of the Necro Cloud nebula. Following the Battle of Altamid, Kirk used a phaser to ignite the ventral thrusters on the wrecked saucer as a way to distract Kalara and Krall's drones by causing it to flip over onto it's dorsal side. This action destroyed the entire bridge upon impact with the surface of Altamid. (Star Trek Beyond)
The captain's chairs on at least two vessels, the Crossfield-class USS Discovery and the Walker-class USS Shenzhou, had a small metal burr on the bottom of the left armrest due to a construction glitch at the San Francisco Fleet Yards. Commander Michael Burnham observed Captain Philippa Georgiou would rub the burr with her thumb during tense moments in order to stay "in the moment," so frequently that Georgiou had worn it down to an indentation. Burnham also observed Saru touching the burr on Discovery, and Ensign Sylvia Tilly touched it as well upon taking command of the ship for the first time. (DIS: "Su'Kal")
When commandeering the Dreadnought-class USS Vengeance, Captain James T. Kirk ordered Admiral Alexander Marcus to vacate the command chair. Marcus refused, even after Kirk threatened him, "I could stun your ass and drag you out of that chair." Marcus hurried out of the chair in an attempt to escape when Khan, who had accompanied Kirk onto the bridge, went on the offensive. After murdering Admiral Marcus and taking control of the Vengeance himself, Khan assumed the command chair, though a detonation aboard the ship hurled him out of it. Immediately following the crash of the Vengeance in San Francisco, Khan was cowering behind the chair, though he soon left it. (Star Trek Into Darkness)
During an honorary tour of the Enterprise-B on its maiden voyage, James T. Kirk – now retired from Starfleet – gave a longing gaze towards the ship's command chair. When Captain John Harriman asked Kirk and his companion Montgomery Scott to take their designated side seats, Kirk was reluctant to leave the command chair, briefly resting an arm atop the back of it, but then did as Harriman had suggested. Kirk later glanced at the chair again, upon advising Harriman, "Risk is part of the game if you want to sit in that chair."
When the ship subsequently became caught in a gravimetric field emanating from the Nexus, the craft shuddering caused firstly Harriman and later Kirk to cling onto the chair. After Kirk and Scott hatched a plan to enable the Enterprise-B to break away from the field, Kirk finally assumed the vessel's command chair while Harriman volunteered to go to main engineering to make modifications necessary for the plan to work. However, Kirk thereafter left the chair, swapping places with Harriman. Harriman thereafter left the chair to investigate a hull breach which had apparently cost Kirk his life.
Kirk had actually been drawn into the Nexus, in which Captain Jean-Luc Picard attempted to recruit him to help stop Tolian Soran on Veridian III. Kirk concluded that the situation he now found himself in, of whether to make a difference again, was "about that empty chair on the bridge of the Enterprise," and he proceeded to assist Picard, actually being killed in the process. (Star Trek Generations)
The Freedom-class starship had a more basic version of the command chair when the USS Franklin was discovered by members of the crew of the USS Enterprise in 2263 of the alternate reality, as it was from nearly 100 years earlier. After James T. Kirk boarded the ship, he was displeased when alien scavenger Jaylah situated herself in the command chair while he was on the Franklin bridge. This caused Montgomery Scott to mouth to Jaylah behind Kirk's back that Kirk liked sitting in the command chair. Later, when launching the Franklin to pursue Krall (somewhat ironically, the Franklin's former captain), Kirk took the Franklin's command chair and remained there during a battle which followed. As the Franklin prepared to fly into the Swarm ships' midst, Kirk grabbed on tight to the armrests of the command chair. (Star Trek Beyond)
In 2364, Captain Jean-Luc Picard showed young Wesley Crusher the command chair aboard the USS Enterprise-D. A panel on the right arm of the chair had been designed for log entries, library computer access and retrieval, viewscreen control and intercoms. The left arm of the chair was equipped with a panel that could be flipped open to reveal backup conn and ops panels, plus armament and shield controls. (TNG: "Encounter at Farpoint")
By 2365, the command chair on the Enterprise-D had been upgraded to a newer version with padded armrests and the replacement of the hidden control panels with permanently open ones. This chair remained on the bridge until the ship's destruction in 2371. In hindsight, Commander Riker subsequently admitted, "I always thought I'd get a shot at this chair one day," referencing his long-held desire to captain the Enterprise, a goal Picard suspected he might still attain. (TNG: "The Child"; Star Trek Generations)
In an alternate timeline in 2366 in which the United Federation of Planets was at war with the Klingon Empire, the bridge of the Enterprise-D featured a more militaristic-looking command chair. Furthermore, unlike the Enterprise of the normal timeline, this chair was not surrounded by seats for the first officer and another officer. (TNG: "Yesterday's Enterprise")
Aboard the USS Kelvin in 2233 of the alternate reality, Captain Richard Robau and Lieutenant Commander George Kirk consecutively occupied the command chair while the Kelvin was attacked by the Romulan mining vessel Narada. Both officers used the chair's intercom but, as the Kelvin crashed into the Narada in a ramming maneuver, Kirk was flung out of the chair. (Star Trek)
Kobayashi Maru Simulator
Gallery of command chairs
On Star Trek: Deep Space Nine, a particular command chair prop was included, over multiple years, in viewscreen appearances of Cardassian Gul Dukat. In DS9: "Return to Grace", a built-up version of the chair appeared aboard the Groumall, a Cardassian freighter commanded by Dukat. ("Oddments", Star Trek: Deep Space Nine - The Official Poster Magazine, No. 12)
An oversized Romulan command chair was built for DS9: "The Die is Cast". "We never shot it," said Laura Richarz, "because it was way too big and very clunky. However, it was thronelike." As a result, the chair was used in DS9: "Ferengi Love Songs", as Grand Nagus Zek's throne at the Chamber of Petitioners in Ferenginar's Tower of Commerce. (Star Trek: Deep Space Nine Companion (pp. 445-446))
The command chair of the Enterprise-E was designed by illustrator John Eaves, who placed the chair a few inches above all the others on the starship's bridge in order to accentuate the captain's position, focusing the bridge design on him. (Star Trek: Communicator issue 110, p. 22)
In a deleted scene from Star Trek Nemesis, the Enterprise-E's command chair is refitted with seat belts. This chair design later served as the command chair for the Enterprise (NX-01) in Season 4 of Star Trek: Enterprise.