Research shows that magpies can display mirror self-recognition behavior. Mirror self-recognition is one of the few tests of behavior that is generally considered to be indicative of the presence of a critical component of consciousness, the ability to recognize oneself. Several of the magpies tested used the mirror to attempt to remove added dots of color on their feathers.
I don’t know all the member species of this club, or all the species that have failed mirror self-recognition. (It should be noted that not every individual of a species must show the behavior, so some negative tests with small numbers of test subjects may not be absolute indicators of capability.) Here are some in each category as I recall offhand, so corrections and additions are welcome:
Mirror self-recognizers (updates marked with *):
Humans (older than about 18 months)
Negative tests of mirror self-recognition:
So far, all the self-recognizers I know of happen to be vertebrates. It is interesting that not all of them are mammals, though, so any theory explaining these cognitive capabilities needs to be expansive enough to account for the different neural architecture of the avian brain.