Stone Mines provide the resource stone in Age of Empires and Age of Empires II. They commonly appear in clumps of 3-10 mines and the stone can be extracted by tasking a Villager on the mine.
Stone is not used in Age of Empires III and Age of Mythology. Hence, Stone Mines don't appear there.
Age of Empires 
Edit
Stone Mines in Age of Empires are fairly common and as such, acquiring stone is not usually a problem. Stone is used to build Towers and Walls.
Age of Empires II Edit
Stone Mines in Age of Empires II are about as common as in Age of Empires although more stone is used and as such the mines run out more quickly, leaving trade as the only available method of acquiring more. Stone is used for building Towers, Walls, Castles, Town Centers, and Wonders and for researching some technologies.
