The Mirror Test is an experiment to gauge whether a species is capable of self-recognition and if they have the potential of self-awareness.
In addition to apes, dolphins, whales, elephants, European magpies, and some species of monkeys have passed the mirror test.
The test and other theories of animal intelligence were discussed on the recent episode of The Nature of Things, “Mysteries of the Animal Mind”.
It was also mentioned on SETI’s Big Picture Science podcast episode “Aware Am I?”.
Update:
Wired has a video about a guy who made a mirror rig for his smartphone camera to take interesting video of primates at the zoo.