Muteness was the inability to speak due to dysfunction of the larynx or as a result of a psychological condition that caused a person to become unable to speak due to trauma or shock. It frequently accompanied deafness. (TNG: "Loud As A Whisper")
The inhabitants of Gamma Vertis IV were all naturally mute, as was Gem. (TOS: "The Empath")
The ruling family of Ramatis III all shared a genetic condition rendering them deaf and mute. One member of the ruling family, the famed mediator Riva, overcame his condition by using a chorus of telepathic aides to speak on his behalf. (TNG: "Loud As A Whisper")
The two Bajoran farmers Baltrim and Keena were rendered mute during the Cardassian Occupation of Bajor. (DS9: "Progress")
In 2372, Chancellor Gowron called Worf a mute d'blok. (DS9: "The Way of the Warrior")