This PLoS Biology paper by Pier Ferrari et al. is highly interesting:
Here we report the behavioral responses of infant rhesus macaques (Macaca mulatta) to the following human facial and hand gestures: lip smacking, tongue protrusion, mouth opening, hand opening, and opening and closing of eyes (control condition). In the third day of life, infant macaques imitate lip smacking and tongue protrusion. On the first day of life, the model's mouth openings elicited a similar matched behavior (lip smacking) in the infants. These imitative responses are present at an early stage of development, but they are apparently confined to a narrow temporal window. Because lip smacking is a core gesture in face-to-face interactions in macaques, neonatal imitation may serve to tune infants' affiliative responses to the social world. Our findings provide a quantitative description of neonatal imitation in a nonhuman primate species and suggest that these imitative capacities, contrary to what was previously thought, are not unique to the ape and human lineage. We suggest that their evolutionary origins may be traced to affiliative gestures with communicative functions.
That's the abstract. The second paragraph of the paper is essential background if you don't know much about babies:
To date, studies of early signs of this matching capacity have been largely limited to human infants. Almost 30 years ago, Meltzoff and Moore  reported that 2- to 3-wk-old infants responded with corresponding matching behaviors to specific human facial gestures, such as mouth opening (MO), tongue protrusion (TP), lip protrusion, and hand opening (HO). Other studies confirmed this early investigation, although there is still considerable debate about which gestures are actually imitated [4-9]. To avoid the possible interferences of early learning experiences with innate imitation processes, Meltzoff and Moore conducted further investigations immediately after birth and demonstrated that newborns also can imitate adult facial gestures [4,5]. They argued that the specificity of the imitative response indicates a capacity to accurately match the body parts involved. Because newborns cannot see their own face but can only perceive it through proprioception, the matching of their own acts to those observed should require a supramodal representation of the observed gesture, called active intermodal matching [3-5,10].
They note later in the paper that some human babies just don't imitate in this way at all. It's pretty striking when you see it happen, so the variation between infants ought to be explained somehow. The most consistent imitation is sticking out the tongue (this may be why we all try to do it to babies!). And there is a window in humans -- starting at around 2 weeks, the imitations last only up to around 3 months.
Ferrari and colleagues explain the windows for imitation in terms of social learning and the development of independence. They note that human infants start to exhibit new social abilities at around 2-3 months such as smiling and cooing. Chimpanzees have a slightly earlier window for imitation than humans, and also start to show independence earlier. The imitation that they observe in the macaque infants ends by 7 days of age -- and they write that the infants start to show motor independence away from the mother for short periods of time by this age:
Already at 1 wk, infant macaques may leave their mother for short periods of time. Infant exploration, involving motherinfant separation, increases over time. In our experiments, we noticed that holding a 2-wk-old or older infant and capturing its attention with the stimulus became more and more difficult with increasing age. In humans and chimpanzees, neonates stay in body contact with their mother for much longer, and the mother is the only one responsible for maintaining the infant. Thus, neonatal imitation in rhesus macaques occurs with a timing that, considering the species-specific patterns of development of motor and cognitive skills, is comparable with those reported for humans and chimpanzees.
There is a lot in the discussion about "imitation" and what it means, and how it varies among species, such as between apes and monkeys. It seems to me that "imitation" is a term that is starting to cause more confusion than it resolves. Lately, the term has been limited to cases of learning where an individual is replicating the behaviors of another individual -- not only the end result, but also all the steps that lead to that end result. But the infant "imitation" quite clearly doesn't require the kind of conceptual learning that instances of "imitation" among older juveniles and adults seems to take.
Here they focus on a possible neural basis for the infant imitation, suggesting that "mirror neurons" may be responsible. "Mirror neurons" are activated both when doing an action and when seeing another individual do the same action. To the extent that these mirror neurons are "pre-wired" to connect visual and proprioceptive inputs, they might spur an individual to "imitate" the actions he or she sees.
Of course, that doesn't really address just how such a system might evolve, or what it's adaptive value might be. Some have suggested that infant imitation mainly functions to "make them cute" to adults, or to demonstrate some kind of incipient ability for social cognition to make it more likely that the mother will provide timely care (i.e., by showing that the child is a good investment because it is neurologically OK).
But I really don't see these explanations accounting for a developmental window. To me, a window implies opening and closing constraints on neural development. To that end, it is very interesting that the end of the window appears relevant to social development.
The real question is whether monkey mothers inspire imitation and look for it in their infants. Knowing this would help test whether the imitation itself is an adaptation or whether it is a side-effect of some developmental process (presumably related to the development of social cognition and signalling). Since there is so much variation among human infants in this quality, I am pretty tempted to think it is not a significant point where behavior rubs against survival. It may better be seen as a portal on aspects of development that manifest later. For instance, it may be a frequent consequence of the wiring of mirror neurons that they have this effect on infants, but the adaptive consequences of the wiring are manifested later as juveniles learn to associate the facial expressions of others with their likely behaviors.
From that perspective, the most significant aspect of the paper is its demonstration that the window in apes, and then humans, has greatly increased in length and is delayed relative to birth. And yet, despite these relatively great changes in timing, it is still after birth. In other words, it appears to show a necessary early environmental role for the development of social cognition (if it's that), which has extended in the ape and human lineages.
It has stuck a long chunk of learning into a developmental process as a trade-off against earlier independence. Of course, social independence and motor independence are different things...
UPDATE (9/7/2006): Brainethics has pictures.
Ferrari PF, Visalberghi E, Paukner A, Fogassi L, Ruggiero A, et al. (2006) Neonatal Imitation in Rhesus Macaques. PLoS Biol 4(9): e302. Free full text