Such self-awareness is rare. Scientists previously believed only humans, apes and dolphins possessed self-recognition skills. All of these animals are highly intelligent and seem to feel empathy, a quality that likely is linked to self-awareness. Many other animals possess self-awareness, a multi-faceted, complex phenomenon, which seems to manifest itself at different levels.
"It may be freely admitted that no animal is self-conscious, if by this term it is implied that he reflects on such points, as whence he comes or whither he will go, or what is life and death, and so forth." - The Descent of Man and Selection in Relation to Sex, Charles Darwin
"Nevertheless, the difference in mind between man and the higher animals, great as it is, certainly is one of degree and not of kind." Thus, there are shades of gray and not black-and-white differences between humans and other animals in cognitive abilities. So, while animals might not ponder life and death the way humans do, they still may have some sense of self. - The Descent of Man and Selection in Relation to Sex, Charles Darwin
After decades of studying animals ranging from coyotes, gray wolves, domestic dogs, and Adelie penguins and other birds, Marc Bekoff, writer of Minding animals: Awareness, Emotions, and Heart, come to the conclusion that not only are some animals self-aware, but also that there are degrees of self-awareness. He argues that a sense of body-ness is necessary and sufficient for most animals to engage in social activities that are needed in the social milieus in which they live.