An exoskeleton was a hard, supportive and/or protective structure that occurred in the external anatomy of many organisms. Most commonly found in invertebrates, such as insects and other arthropods, exoskeletons were also found on some sentient lifeforms.
Tholians possessed exoskeletons composed primarily of minerals, and were susceptible to cracking or even shattering at temperatures that were lower than their natural tolerances. (ENT: "In a Mirror, Darkly")
Rasiinians featured a bony exoskeletal plate that covered their faces.
Klingons had an exoskeleton that encased their cranium. This protective structure had a feature called the tricipital lobe. (TNG: "Descent")
Although Klingons are stated to possess a cranial exoskeleton, it seems apparent that this structure is not outside of their skin like a typical exoskeleton would be. This may indicate that a Klingon's cranium actually features two distinct layers of bone, and "exoskeleton" is used to distinguish the outer layer, which is likely where their well-known cranial ridges are found. This would offer extra protection to the brain (except at the vulnerable tricipital lobe), and seems to fit in very well with the Klingon principle of Brak'lul.
Borg drones were fitted with artificial exoskeletons known as exo-plating. This protective layer was sometimes installed directly over the clothing and equipment that the drone had been wearing when it was assimilated. (Star Trek: First Contact) Borg exo-plating was extremely durable; even the residual exoskeleton on Seven of Nine's left arm was capable of withstanding five million gigawatts of power. (VOY: "Revulsion")