When mined, they will drop a Gem and 1 Thulecite plus a 5% chance of 1 extra Thulecite. The color of gem that drops will be the same type that appears on the statue, either in the staff or at the base. If the statue does not have a gem embedded in it, it will drop Nightmare Fuel in its place.
In Don't Starve, the color changes with each Nightmare Cycle or simply when reloading the game. This makes it possible to choose which gems the statues will drop when mined; gemless statues will remain gemless however.
The appearance of the statues change depending on the current phase of the Ruin's Nightmare Cycle. They emit light during all phases, except "Calm". At the most intense state, the statues will be covered in Nightmare Fuel and gain a hazy glowing quality (though their light radius does not increase). If mined during the Nightmare phase, there is a 30% chance for a Terrorbeak or Crawling Horror to spawn.
In A New Reign for Don't Starve Together, a new variant of the Ancient Statue can be found in the Atrium Biome, lacking gem sockets and having a rather organic appearance. Instead of transforming at the peak of the Nightmare Cycle, it will change its state when the Ancient Gateway is activated. This version of the statue can not be destroyed. By killing the Ancient Fuelweaver, all Ancient Statues will respawn in their locations, making them renewable.