From Romulus and Remus forward, there have been a number of accounts of wolf children or feral children raised by wild animals or out of human contact. These accounts exist mostly in anecdote and hearsay as well; but most of them affirm that these children never learned to speak a language, or learned it imperfectly. There have also been accounts of twins who spoke an unintelligible language only their sibling understood. These cases are better documented; in the 1970s, the Kennedy twins whose given names were "Grace" and "Virginia" called each other Poto and Cabengo; it was determined that their idiosyncratic speech was a deeply altered form of English, with some influence from their grandmother's German. It appeared to be a well-formed language, with rules governing grammar and syntax. Similarly idiosyncratic speech patterns were reported from the twin writers June and Jennifer Gibbons.
Even in the absence of the unusual social lives of twins, many people have found it relatively easy and natural to construct new languages, with lexicons either derived from pre-existing languages, or wholly imagined; the author J. R. R. Tolkien and his several languages of Middle-earth is one well known creator; there are many others. Contact languages spontaneously arise when people speaking dissimilar languages must mingle with each other for sufficient periods. These contact languages, or "pidgins," give rise to "creoles" if they become mother tongues in their own right. All of these creations also bear witness to the fact that the use and acquisition of language is a human trait that can manifest itself spontaneously, without formal instruction, and under adverse circumstances.
The recent development of Nicaraguan Sign Language starting in 1979 seems to be an independent invention of language from scratch. "It's the first and only time that [linguists have] actually seen a language being created out of thin air." - however it may be connected to paralinguistic gestures used by spanish-speaking Nicaraguans as part of their language.