Psychologists (and philosophers) have argued that mimicry is a key learning tool that humans use to understand other people and, as they grow, begin to understand human emotions. Since such mimicing activity starts very early, in infancy, it has been seen as a genetically determined capacity.
But how far back in human ancestry does it go? Via Majikthise (love that name, and Lindsey is hot), we see footage of Italian primatologists very easily engendering mimicry from baby Macaque monkeys less then 10 days old. See the movie here, a more hi-res version here, and an example of '"tongue protusion" mimicry here. Also, you can read about the experiments here.