This reminds me of one of my favourite neuropsych experiments.
Basically you put a dot of sweet food stuff, like icing, one a monkey or an ape's (or a person's) forehead without them noticing and stick them in front of a mirror. Monkeys up to gibbons I think and children under the age of about two won't correlate what they see in the mirror with themselves so if they interact with it at all they'll try to take the food off the mirror or reach behind/through the mirror to get at it. Apes (and older humans, obviously) will see their reflection and reach to the spot on their face where the food is.
I can't find the video from the lecture where I heard it originally but
this is fairly similar.
The cool thing is that if you follow the phylogenetic tree in primates after a certain point all the 'more evolved' species can do this and the ones up that point can't, which means there was a definite that a past ancestor acquired the ability to be self aware, the same way one acquired opposable thumbs. Point being that a polar bear probably doesn't have the right brain bits to be self aware enough to cover their nose, but a chimp might, which I think is cool.