–Wurt
Gears are Items dropped by Clockwork Knights, Clockwork Bishops, and Clockwork Rooks. They can also be found by digging up Graves (chance of 3.07%).
Gears can be used to build an Ice Box and a Divining Rod, as well as boost the max stats of WX-78 by simply consuming them. In the Ruins, repairing Broken Clockworks with 3 Gears will spawn a friendly damaged chess monster (Damaged Bishop, Damaged Knight, or Damaged Rook).
Clockwork Knights, Clockwork Bishops, and Clockwork Rooks and their broken counterparts will not respawn, nor will graves after being dug. Therefore, Gears are a non-renewable resource in the base game.
Downloadable Content
In the Reign of Giants DLC, renewable Tumbleweeds have a chance to drop Gears, thus making gears renewable in this DLC. Also, there are significantly more Chess biomes on a map, including some with Gears lying on the ground, making Gears much easier to get.
In the Shipwrecked DLC, Floaty Boaty Knights drop Gears, thus making gears renewable in this DLC. These are currently the only reliable source of Gears in this DLC. Each Floaty Boaty Knight drops one to three Gears. There is also a small chance of obtaining Gears from digging Sandy Piles, using the Slot Machine, or digging up X Marks the Spot chests spawned by Message in a Bottle. Gears can be used to craft the Quacken Drill and to restore the durability of the Iron Wind by 25%.
In the Hamlet DLC, Gears drop from clockworks that guard Stone Thing. Gears can be bought in 'The Sty' Oddities Emporium for 10 Oincs. They are also dropped by killing Large Iron Hulk. The last two ways makes them also renewable in this DLC.
Don't Starve Together
By killing the Ancient Fuelweaver and regenerating the Ruins, a renewable source of gears becomes a possibility. All Broken Clockworks will respawn upon regeneration. This can become a very efficient source of gears in the later game, as long as the process is repeated often.
There are other ways to get gears that are less viable. The clockwork statues when hammerd in a full moon to get a clockwork form the coresponding statue.