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 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")