Peter Pan Syndrome is the expression commonly used to describe certain people, usually of high intelligence, who cannot face the outside adult world, and who, despite physical evidence of the contrary, keep seeing themselves as children, emotionally and socially.
In short: "they don't want to grow up", and want to stay in Neverland for the rest of their life.
Although I was unable to find any serious documentation of the Peter Pan syndrome as such in official scientific papers, it is commonly referred to in folk psychology and is often used by independent psychotherapists as an established and well-described medical condition with a very strict frame of application and manifestations:
First of all, they all make a clear distinction between Peter Pan syndrome (PPS) and other, more serious, mental conditions involving adults who behave as children both emotionally and mentally. It is more or less established that people suffering from Peter Pan syndrome are mentally fully developed adults who often carry professional activities requiring strong intellectual skills (such as software development or fundamental research...).
Despite their status as physically and intellectually fit adult, they refuse to take on the responsibilities and emotional bearings of adulthood, often immersing themselves with children (typically not theirs) at work or at home, in hope of being accepted as "one of them".
While it is easy to dismiss every emotionally unavailable immature manipulative asshole under this category, it would be inaccurate. In the case of PPS it must be made clear that sex or any physical contact in a sexual way, is perceived as something mildly disagreeable at best... truly repulsive and unbearable for most.
For the same reason, the common association between PPS and pedophilia is an unfair and unfounded one. While the latter demonstrate an attraction to children with clear sexual intent as an adult, PPS is merely an attempt to be considered as a child, thus without the slightest feeling of adult sexual connotation. In fact, the most extreme cases have been known to spontaneously ask for medical castration in order to escape this unwanted aspect of their physical maturation (usually not granted for ethical reasons). Pedophilia and "inappropriate" conduct towards children being such a sensitive topic for obvious reason these days, it is rare to see these people being subjected to a cold-headed rational analysis or given any benefit of the doubt in such situations (cf. Michael Jackson's media case). Then again, it is hard to rationalize in such context and quite understandable to set arbitrary boundaries that should not be transgressed regardless of the motives.
Some psychologists also point out the unfair treatment of genders in this issue: according to them, the inaccurate perception that PPS is essentially a male condition is only spawned by social filters that tend to excuse more easily similar behaviours by women (dismissing them as maternal instinct). Whether justified or not, it is a common trait of society to consider normal for a woman to spend most of her adult life among children, while this would be deemed abnormal and most likely frowned upon in the case of adult or young adult males. This might draw its origin from the old-time misogynist conception that women were somewhat emotionally crippled and closer to children than men in this regard.
Quite expectedly, the first and most notorious case of PPS would have to be none other than Peter Pan's own father: James Barrie, who seems to have projected most of his own issues with adulthood in his literary masterpiece (see his bio for more details).
Once again, while Peter Pan syndrome is a common expression used to label, more or less accurately, serious Peter Pan wannabes, it is not officially sanctioned by the international scientific community (to the best of my knowledge, but feel free to correct me if you know otherwise).
Note: this description of the Peter Pan syndrome is not to be mistaken with the other popular "I can fly, I can Fly" syndrome, often referred to as Superman Syndrome or "maybe I shouldn't have swallowed both the pink and the yellow ones" Syndrome.