A coma is an unresponsive state of unconsciousness.
In 2377, Doctors Elizabeth Lense and Sarjenka of the USS da Vinci put Crewman Fabian Stevens into a coma, in order to deprive the Ardanan parasite that had infected his brain of any stimuli, thus killing it off. (CoE eBook: Signs from Heaven)
Shortly before the Borg Invasion of 2381, Captain Elias Vaughn fell into a coma after being injured in an attack on the vessel he commanded. The Captain was taken to Deep Space Nine for treatment by Doctor Julian Bashir; however, Bashir was unable to revive Vaughn. Vaughn was still in a coma in August, 2382, with prospects for recovery dim. Vaughn's daughter Prynn Tenmei - who remained at Vaughn's bedside during his treatment - ultimately accepted Doctor Bashir's recommendations that she deactivate the life support system keeping Vaughn alive. Vaughn was found to be able to breathe on his own. (ST - Typhon Pact novel: Zero Sum Game)