The mirror self-recognition test (MSR).

Probably most of you might have heard of the mirror self-recognition test (MSR), developed in 1970 by psychologist Gordon Gallup Jr as a method to judge if animals are aware of themselves, respectively know who they are.^[1]

There exist several variations of this test but the principle is always more or less the same: the test animals are getting marked without noticing it, for example by painting them a colorful spot on their face or using a sticker while they are anaesthetized. Later they are placed in front of a mirror to observe their behavior.

Most animals either attack, greet or ignore their own mirror image which means they don't recognize themselves. However, a few species remove the mark from their own face which is a clear hint that they recognize themselves in the mirror. It is controversial discussed what exactly we can deduce from a passed mirror test.

https://files.peakd.com/file/peakd-hive/jaki01/EoyPXLR8MKoCDxTkNDpHCAZ2CeDf1B3zduxHcZskE89ZR4ttfGLKfJcCKqvJ1HfEo9v.jpeg

Source: by Georgia Pinaud, Lille, France.

Which animals are able to pass it?

Species which have passed the mirror test^[2] are:

The great apes bonobos, chimpanzees, orangutans and gorillas in general pass the mirror test, whereby not every single individual is successful. Especially many gorillas have failed. One possible reason could be that these animals normally avoid eye contact so that they may just not look long enough to recognize themselves in the mirror. Other reasons are discussed as well, where one of them could be that gorillas react very sensitively when they feel being observed. "Ironically, it may have been the gorillas' very capacity for self-consciousness that prevented them from exhibiting behaviours indicative of self-recognition in the test situation."^[3]
(Other than great apes, rhesus monkeys don't realize whom they see in a mirror, but can learn it after some practicing.^[4])
Asian elephants are able to pass the test,^[5] whereas again not every single individual passes. One explanation could be that elephants just don't care so much to remove something unnatural from their body.
Bottlenose dolphins behave uncommon in front of a mirror like making repetitious head circling, sticking out their tongues, and inspecting the marking.^[6]
Orca whales seemed to anticipate that their images would look different than before after being marked which also indicates that they knew very well to see themselves in the mirror.^[7]
Some birds like Eurasian magpies^[8], pigeons^[9] and keas^[10] have passed the mirror test, as well.
It is not yet fully clear if also giant manta rays are self-aware. In front of a mirror contingency checking and self-directed behaviors have been observed.^[11]
Do you still remember my series about the "Intelligence of insects", part I^[12] and part II^[13]? Then you may be a little bit less surprised that at least ants ot the genus Myrmica seem to be able to pass the mirror test as well! While watching other ants through glass didn't affect them, in front of a mirror they showed unusual behavior like turning their heads back and forth, shaking their antennae as well as retreating and reapproaching the mirror. Finally they tried to remove blue marks from their clypeuses (instead to attack this strange blue ant) which is a clear sign of self-awareness. Online the source "Marie-Claire Cammaerts, Roger Cammaerts. Are ants (Hymenoptera, Formicidae) capable of self recognition? // Journal of Science. 2015. V. 5 (7). P. 521–532." is only available in Russian.^[14]

Of course the list of self-recognizing animals may get longer after more research has been done.

What about strange creatures like humans and robots? :-)

Human babies definitely pass the mirror test when they are between 20 to 24 months old.^[15]

Finally I would like to cast a very short glance into the sector of artificial intelligence. Has the aim of creating self-aware robots already been reached?

There is research on robots 'recognizing themselves' in a mirror - just build your own opinion, but in my eyes that's not yet comparable with what we are capable of.^[16]

Maybe even more interesting is that at Ransselaer Polytechnic Institute in the US a robot has passed another classic self-awareness test (where no mirror comes into play): three "Nao robots" were programmed to think that two of them were given a "dumbing pill" (in reality a button on top of their heads is responsible for the pill-effect). And indeed, two robots got 'pills' which made them silent, whereas the third pill was a 'placebo'.
Then the robots were asked which kind of 'pill' they had received. Of course only one of them was able to answer ... First it replied "I don't know", but then immediately corrected his answer "Sorry, I know now, I was able to prove that I was not given the dumbing pill."
That's nothing special at all? For a machine it is: being able to give the correct answer requires to listen and understand a question, to hear and recognize its own voice and then understand that one himself can be the only one amongst the robots which must have spoken and thus has received the 'placebo'.^[17]

Dogs pass the sniff test instead of the mirror test.

We have to be careful when interpreting the results of mirror tests! As egocentric humans we tend to consider ourself as the measure of all things which can lead to wrong conclusions.

One example are the results of dogs in the mirror test. To make it short: they fail, and initially scientists concluded that our companion animals are just not self-aware. However, other than us, dogs perceive a bigger part of their sensory input not through their eyes, but by their ears and especially their sensitive noses ... but a mirror image neither barks nor smells like a dog.

Meanwhile dogs have redeemed their good reputation: as scientists recently have shown, dogs react if their own olfactory 'image' was modified. They are "investigating their own odour for longer when it had an additional odour accompanying it than when it did not. Such behaviour implies a recognition of the odour as being of or from 'themselves'".^[18]
Not taking into account that dogs recognize themselves by means of their smell (not of their look) resulted in the wrong assumption they had no consciousness of self.

Sources:

https://en.wikipedia.org/wiki/Mirror_test
http://www.animalcognition.org/2015/04/15/list-of-animals-that-have-passed-the-mirror-test/
http://www.animal-rights-library.com/texts-m/patterson01.htm
https://www.eurekalert.org/pub_releases/2015-01/cp-mcl010215.php
http://www.pnas.org/content/103/45/17053
http://www.pnas.org/content/98/10/5937.full
http://www.sciencedirect.com/science/article/pii/S0376635701001346?np=y
http://journals.plos.org/plosbiology/article?id=10.1371/journal.pbio.0060202
http://onlinelibrary.wiley.com/doi/10.1002/jeab.112/abstract
http://www.diss.fu-berlin.de/diss/servlets/MCRFileNodeServlet/FUDISS_derivate_000000014958/Dissertation_Rahde.pdf
https://link.springer.com/article/10.1007%2Fs10164-016-0462-z
https://peakd.com/science/@jaki01/intelligence-of-insects-part-i
https://peakd.com/science/@jaki01/intelligence-of-insects-part-ii
https://elementy.ru/novosti_nauki/432881/Muravi_sposobny_uznavat_sebya_v_zerkale
http://www.thoughtfulparent.com/2009/10/child-psychology-classics-mirror-test.html
http://www.bbc.com/news/technology-19354994
https://www.sciencealert.com/a-robot-has-just-passed-a-classic-self-awareness-test-for-the-first-time
https://www.eurekalert.org/pub_releases/2017-09/nrts-tst090517.php