A coma (or comatose state) was a state of unconsciousness in which a person was unresponsive to physical stimulation due to a reduction of neurological activity in the neocortex.
A coma could be the result of many things including head trauma and Iresine Syndrome. (TNG: "Violations")
In 1986, following a fall onto a barge from the aircraft carrier USS Enterprise, Pavel Chekov's middle meningeal artery was torn. This internal injury placed Chekov into a coma. (Star Trek IV: The Voyage Home)
In 2152, Jonathan Archer warned Trip Tucker that he could lapse into a coma if he fell asleep while suffering from heatstroke. Tucker thought going into a coma "sounds nice". (ENT: "Desert Crossing")
In 2153, Doctor Phlox placed the crew of Enterprise NX-01 in a comatose state while the starship traversed a trans-dimensional disturbance. This was done in order to dampen the crews' brain activity, as the affected region would disrupt the neocortex of the Human brain. (ENT: "Doctor's Orders")
In 2154, Phlox held Corporal Askwith in a coma because of his cranial injuries he suffered from an explosion of a bomb in the United Earth Embassy on Vulcan. (ENT: "The Forge")
In 2257, Hugh Culber placed Paul Stamets in a medically-induced coma to protect his brain functions after he was badly injured. (DIS: "Such Sweet Sorrow, Part 2")
Comas could be induced to prevent an individual from waking up and causing destruction. In 2259 of the alternate reality, Doctor Leonard McCoy instructed his staff to keep an Augment in an induced coma and put a newly dead James T. Kirk in the Augment's cryo tube to preserve Kirk's brain functions. (Star Trek Into Darkness)
In 2267, the invalid Christopher Pike kept blinking "no" via his wheelchair. According to Leonard McCoy, upon being asked to specify which question he was responding in the negative to, Pike almost agitated himself into a coma. (TOS: "The Menagerie, Part I")
In 2268, McCoy characterized John Gill's state as almost comatose. (TOS: "Patterns of Force")
In 2285, Torias Dax was in a fatal shuttle accident. He was said to have fallen in a six-month coma before dying, but in fact, he had died quickly, and had the Dax symbiont transferred to Joran Dax. (DS9: "Equilibrium")
In 2366, Doctor Beverly Crusher induced coma in Deanna Troi to shield her from all outside stimuli as she was affected by the music planted into her mind by Kevin Uxbridge. (TNG: "The Survivors")
In 2367, a simulation of Crusher told Will Riker that a strain of Altarian encephalitis had resulted in his entering a ten-day bout of coma and delirium. (TNG: "Future Imperfect")
In 2368, several crewmembers of the USS Enterprise-D, including Counselor Troi and Commander Riker, fell into comas as a result of an invasive telepathic memory attack performed by Jev, a member of the visiting Ullian historian delegation. (TNG: "Violations")
In 2369, Zek, the Ferengi Grand Nagus, used the Dolbargy sleeping trance, a voluntarily-induced deep coma, to fake his own death when he wanted to test the readiness of his son, Krax, to serve as Nagus. Zek's servant, Maihar'du, had taught him the technique. (DS9: "The Nagus")
In 2371, Julian Bashir was attacked by a Lethean named Altovar, who wanted to steal controlled medical equipment. Bashir was left in a coma, during which he experienced a disturbing hallucination involving aging rapidly. (DS9: "Distant Voices") In that same year, Neelix on the USS Voyager fell into a coma after he had his lungs removed by a Vidiian. (VOY: "Phage")
In 2372, Benjamin Sisko sustained severe trauma to the head as a result of a Jem'Hadar attack. Kira Nerys attempted to prevent a coma by keeping him occupied with conversation. (DS9: "Starship Down")
In 2373, an accident left Jadzia Dax, Elim Garak, Odo, and Benjamin Sisko in comas. Residual morphogenic enzymes in Odo's brain created a telepathic link between the four, through which they relived a disturbing memory of Odo's during the Occupation of Bajor. (DS9: "Things Past").
In the same year, Kes fell into a coma and Captain Kathryn Janeway attempted to save her life by going through a Nechani ritual. (VOY: "Sacred Ground")
In 2376, Lieutenant B'Elanna Torres was left in a coma caused by a shuttle accident. She experienced hallucinations relating to her Klingon heritage. She later recreated the conditions of the accident in order to return to the hallucination in an attempt to free her mother form Gre'thor. (VOY: "Barge of the Dead")