Humans do it, great apes do it, dolphins do it, now elephants (also here) have also been shown to do it - recognize themselves in the mirror, i.e., realize that the image in the mirror is the image of themselves and not a strange animal. That's a biggie in the world of cognitive science and the study of evolution of consciousness:
When the mirror was unveiled in their yard, they immediately walked over and began poking and prodding and inspecting and playing. They used their trunks to inspect it and then themselves. Two got on their hind legs to look on top of the mirror. One got on the ground to inspect the bottom of it. They opened their mouths, exploring an area of their body they were familiar with but had never seen. They even brought their food over to eat in front of the mirror.
"All three of the elephants demonstrated this self-directed behavior," said Joshua Plotnik, a co-author of the study and a graduate student at Emory. And like children inspecting their own bodies, the elephants put their eyes right up to the mirror, seemingly to figure out what it was and how it worked, he said. Then they investigated parts of their bodies they had never seen. They grabbed one of their ears and pulled it towards the mirror for inspection. "These are behaviors that they don't normally do," he added.
The scientists used a non-toxic paint to mark a small spot on one side of each animal's forehead, which would be visible when it looked in the mirror. They also marked an identical spot on the other side of the forehead, but invisible paint was used to test whether the animals were seeing rather than feeling the mark.
Happy was the only one of the three who noticed the spot and used her trunk to examine it -- over and over again. She did not go after the invisible spot on the other side of her forehead.
I recollect a fossil find that tied whales and elephants to some early shared branch of mammal evolution. [and my memory could be as faulty as my diligence in checking this "fact"]
Dolphins are among the "mirror test" graduates but not whales...now for the whale experiment.
The whale taxonomy and evolution has been revised several times over the past couple of decades. Even I am confused as to what the current thinking is right now! Darren Naish of Tetrapod Zoology blog and Carl Zimmer of The Loom have written about whale evolution recently and may know better, but if I remember correctly, the elephant-whale connection is a goner for good.
whales are closer to hippos.
'course if you go back far enough...