In addition to humans, adult chimpanzees, bonobos and orangutans, elephants seem to have a concept of self (however minimal):
Elephants can recognize themselves in a mirror and use their reflections to explore hidden parts of themselves, a measure of subjective self-awareness that until now has been shown definitively only in humans and apes, researchers reported yesterday.
The findings confirm a long-standing suspicion among scientists that elephants, with their big brains, complex societies and reputation for helping ill herdmates, have a sufficiently developed sense of identity to pass the challenging “mirror self-recognition test.”
The test, which in this case required construction of a huge, “elephant-proof” mirror at the Bronx Zoo, where the experiments were conducted, provides an index of an animal’s ability to conceive of itself. It is a quality of self-consciousness that some scientists believe is a prerequisite for the emergence of empathy and altruism.
Such animals, the thinking goes, are in a position to use what they know about themselves to make inferences about other beings and their needs.
More at The Washington Post.