Other than humans, what animals are self-aware?
The best test for self-awareness that we have right now is called the ‘mirror test.' It involves introducing an animal to a mirror, then placing a mark somewhere on the animal's body (using the face) where it can only see the mark using the mirror.
If the animal touches the mark on its own body when looking in the mirror, we know that the animal understands that it is looking at an image of itself. And that's only possible if the animal is aware of itself.
Human babies begin to grasp the concept around 13 to 20 months, and most infants pass the test by 24 months.
Among other species which have been tested, the following pass the test:
European Magpies (yes - a small bird passed the test - it is self aware!)
There are a great many potential species which have not yet been tested.
Dogs, sea lions, giant pandas, and several species of monkeys have failed, so far. However, failure of the mirror test does not necessarily indicate lack of self-awareness. The test can prove self-awareness, but it cannot disprove it. Some animals, such as pigs, may simply not care about a dot on their face, for example... :)
And some infants older than 24 months fail the mirror test, but show other signs of self-awareness. So perhaps one day we'll come up with are certain test.