The stress response, which involves joint activity of the nervous and endocrine systems, is one of the basic adaptive mechanisms that ensures the survival of the individual. The activation of the sympathetic nervous system, the sympathetic-adrenal-medullary axis, and the hypothalamic–pituitary–adrenal axis enables organisms to respond to endogenous and exogenous challenges. Repeated short-term stress leads to long-term stress, which disrupts physiological homeostasis. Unlike domestic animals, wild animals are not protected from environmental and weather influences or treated for diseases. In addition, climate change, habitat fragmentation and loss, and urban stressors (such as light, noise and chemical pollution; xenobiotics; traffic; and buildings) affect individual wildlife and populations. In this review, we have attempted to depict the magnitude of the stress response in wildlife and related domestic animals as well as in captive and free-ranging animals. The intensity of the stress response can be estimated by determining the concentration of glucocorticoids in body fluids, tissues, and excreta. A comparison of results from different studies suggests that domestic animals have lower fecal and hair glucocorticoid concentrations than related wild animals. Additionally, fecal and hair glucocorticoid concentrations in captive animals are higher than in free-ranging animals of the same species. As there are limited data on this topic, we cannot draw definitive conclusions about glucocorticoid concentration and stress response. Further studies are needed to clarify these issues.