A coma (or comatose state) is a state of unconsciousness in which a person is unresponsive to physical stimulation due to a reduction of neurological activity in the neocortex.
In 2153, Phlox placed the crew of the Enterprise in a comatose state while the starship traversed a region of transdimensional space. 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 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 2368, several crewmembers of the USS Enterprise-D, including Counselor Troi 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 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, where 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 2373, a shuttle accident left Jadzia Dax, Elim Garak, Odo and Benjamin Sisko in a coma. Residual morphogenic enzymes in Odo's brain created a telepathic link between the four, where they relived a disturbing memory of Odo's during the Occupation of Bajor. (DS9: "Things Past").
In 2376, Lieutenant B'Elanna Torres was left in a coma, also caused by a shuttle accident. She experienced hallucinations relating to her Klingon heritage. She later re-created 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")