Humans are unlikely to be the only animal capable of self-awareness, a new study has shown. (Link)
I believe all animals have some sense of self awareness. Charles Darwin also believed this and I recently read a comment from an article I liked:
"Darwin did believe that animals had some sense of self, and also championed the notion of evolutionary continuity, leading him to also write, "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"
There must be a scale of self awareness. And perhaps we are not yet at the highest level of that self awareness. Perhaps some animals (dolphins?) or aliens that have evolved further than us have an even higher/different level of self awareness? Just thinking out loud there.