Psychologists have a test that's generally agreed to show whether a child or an animal has self-consciousness. Someone will put a red dot on their forehead while they're asleep and then see what happens when they look in a mirror. If orangutans, say, can put their hand on their forehead when they see a red dot on the forehead of the image of the orangutan in the mirror, it's supposed to show that the orangutan is thinking, "Hey, that's me, and I've got a red dot on my forehead."
I've been thinking about this, and I'm not so sure. Doesn't it really just show that they expect a correlation between things in mirrors and things that we know mirrors reflect? I wonder about this as I see my kids learning to identify themselves in the mirror. They might easily first get the concept that the things in the mirror match up with the things outside the mirror, long before they start thinking "that's me in the mirror". So why are these tests supposed to tell us that orangutans, gorillas, and chimps have self-consciousness? Maybe they do, but I can't see how this test should show that.
Update: Chris says there are other experiments that do show this (see comment below). If so, my point still stands. You need to have a different experiment to rule out the possibility I presented.