There are several types of behavioural evidence in favour of the notion that many animal species experience at least some simple levels of consciousness. Other than behavioural evidence, there are a number of anatomical and physiological criteria that help resolve the problem of animal consciousness, particularly when addressing the problem in lower vertebrates and invertebrates. In this paper, I review a number of such behavioural and brain- based evidence in the case of mammals, birds, and some invertebrate species. Cumulative evidence strongly suggests that consciousness, of one form or another, is present in mammals and birds. Although supportive evidence is less strong in the case of invertebrates, it is more likely than not that they also experience some simple levels of consciousness.