A coma is an unresponsive state of unconsciousness.
In the early 2250s, Yannid VI's Prince Arlph was kidnapped by rebels. A young James T. Kirk from the starship USS Republic led the search team that found him, but Kirk's weapon discharge ricocheted into Arlph, putting him into a coma for the next several years. Decades later he would conspire to ruin Kirk. (TOS comic: "The Enterprise Murder Case!")
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. He was taken to Deep Space 9 for treatment by Doctor Julian Bashir; however, he was unable to revive Vaughn. By August 2382, Vaughn was still in a coma, with prospects for recovery dim. Vaughn's daughter Prynn Tenmei, who remained at his bedside during his treatment, ultimately accepted Bashir's recommendations that she deactivate the life support system keeping Vaughn alive. However, Vaughn was found to be able to breathe on his own. (ST - Typhon Pact novel: Zero Sum Game)