Deafness is the state of being unable to hear, whether by genetic makeup, congenital defect, or external damage to a being's hearing. Some societies (such as the Ferengi) consider deafness a weakness or handicap, while others have no social stigma attached to it.
Many well-known beings throughout history have been deaf, including eighteenth century Earth musician and composer Ludwig van Beethoven, and twenty-fourth century mediator Riva. (TNG: "Loud As A Whisper")
In 2267, an aging Robert Johnson initially had some difficulty hearing Captain James T. Kirk address him. Later in the USS Enterprise sickbay when Kirk asked if he could hear him, he replied that he was not deaf yet. Shortly after, Lieutenant Galway experienced hearing difficulties following her exposure to the radiation on Gamma Hydra IV. When she told Dr. Leonard McCoy about it, he suggested hypersonic treatment and told her not to worry. (TOS: "The Deadly Years")
In 2373, Quark became temporarily deaf in his right ear after being stranded on a cold Class L planet with few provisions. He explained to Odo that a one-eared Ferengi was considered only half a man. (DS9: "The Ascent")
In a vision sent to Benjamin Sisko by the Prophets and the Pah-wraith, Benny Russell encountered a preacher who quoted a passage from the Bible's book of Isaiah: "Then the eyes of the blind shall be opened, and the ears of the deaf shall be unstopped." (DS9: "Far Beyond the Stars")