That depends on how you define 'witch'. The belief that there exist people within the community who are able to cause harm by magical means has existed throughout virtually all cultures and time periods. The function of witch beliefs in a society has sometimes been described as a sort of release valve for the social and economic tensions within a community, as a way of both explaining and resolving perceived hardships.

Our modern image of the conical-hatted, broomstick-riding witch is heavily rooted in what historians call the 'cumulative concept of witchcraft', which emerged in late medieval Europe as a sort of mish-mash of folk superstitions and elite ideas about the devil, magic, and heretical conspiracies. Brian Levack identifies some of the main features of the 'cumulative concept of witchcraft' as: The pact with the Devil, the Sabbat, flight, and animal metamorphosis. I'll try and give a quick rundown of these features here, though it's important to bear in mind that the concept of 'cumulative witchcraft' was not fully realised everywhere at every time, and nor was its reality accepted by everybody.

The diabolical pact was believed to be the source of the witch's power. The idea that an individual could make such a pact appears in the writings of St. Augustine, and by the 12th century the idea had become strongly associated with magic and sorcery. In medieval times, however, accusations of diabolical magic were largely reserved for elite magicians, who comprised what Richard Kiekhefer has described as a 'clerical underworld' of necromancers and occult practitioners. It wasn't until later that the pact became associated with our familiar 'village witch'.

The Sabbath or Sabbat was imagined as a nocturnal meeting of witches where they would collectively worship the devil. The exact details of the Sabbat differ between trials, but typical activities witches were thought to indulge in include ritual sacrifice, cannibalism, orgies, putrid feasts, weather magic, and sex with the devil. The Sabbat is closely linked to flight and animal metamorphosis, which were said to be the witch's preferred mode of transport to these diabolical meetings.

Taken individually, there was nothing particularly novel about any of these ideas. As demonstrated by Norman Cohn in his Europe's Inner Demons, the nocturnal gathering of religious deviants has its roots in the Roman Empire, where early Christians were accused of meeting up in order to eat the flesh and drink the blood of newborns in a gruesome misinterpretation of the Eucharist. Later Christians appropriated this stereotype, and reflected it onto heretics, lepers and Jews. Heretics and Jews are especially relevant here, as both groups had become strongly associated with diabolical magic. Early (14th-15th C) witch trials were almost indistinguishable form heresy trials, and Sabbats were sometimes referred to as 'synagogues' in these early years of witch persecution.

Folklore also fed into the stereotype. There are scattered records that suggest the survival of certain pre-Christian superstitions and beliefs among the lower orders of society. These records come in the form of trials and law codes, and often take a sceptical view. For example, an early medieval Germanic law code forbids the killing of women accused of metamorphosing into Strigae - owl-like creatures of Greek legend believed to kill children. The 10th Century Canon Episcopi condemns "certain wicked women, turned back toward Satan, seduced by demonic illusions and phantasms, believe of themselves and profess to ride upon certain beasts in the nighttime hours, with Diana, the Goddess of the Pagans". This seems to be connected to a whole matrix of medieval folk beliefs concerning a hidden society of 'good women' or 'good neighbours', who, under the guidance of a maternal figure known variously as Richella, Horiente, Holda or 'the mistress of the good game', among others, would convene at night time and go from door to door feasting and dining in peoples' cellars. Inquisitorial trials have been uncovered that strongly indicate that there were individuals who were fully convinced that they genuinely partook in such fanciful activities. Beliefs of this nature were strong enough that even in modern times, people in remote parts of Europe would leave out plates of food to please the 'good ladies'.

It is important to remember that belief in the ability of one individual to harm another by magical means had probably always existed among the lower orders of society, and it was this harmful magic (maleficium) that was the chief concern of those who believed themselves to be the victims of witchcraft. Elite ideas about Sabbats and diabolical conspiracies don't seem to have featured much in the minds of the peasants who brought accusations against their neighbours.

So, the concept of the 'witch' that came about in late medieval Europe was an amalgamation of elite and popular traditions. One could argue that all that was required for the stereotype to come about was for the elites to abandon their scepticism and take reports of night flying women seriously, and then merge these stories into their own conceptions of magic, heresy and demonology. This fusion seems to have taken place in the Alpine regions around 1430, though mass persecutions did not start until the late 16th century.

As for the physical depiction of the witch, something we would recognise as a stereotypical witch began to appear in woodcuts from the 15th century. The earliest known depiction of a witch in flight dates from c.1489, and is featured on this page. By the 17th century, we get depictions that are very familiar to us. The ubiquitous broomstick was one of many modes of transport believed to be used by witches. We also find examples of magical flight on distaffs, pitchforks, sticks, monsters, spoons, or blades of grass. Another common motif, that of the black cat familiar, has multiple origins. The idea that witches kept animal familiars is peculiar to English witch trials, and while cats are a common example, dogs, rabbits, frogs, mice, and other creatures also crop up with varying frequency. In 19th century England, rodents seemed to predominate in folk superstition. Black cats had more specifically evil connotations in continental Europe, where it was commonly held that the devil would take the form of a black cat when appearing at the Sabbat. The black cat motif is probably a fusion of these two ideas.

That's about all I can summon up at the moment. Some of my sources are:

Wolfgang Behringer, Witches and Witch Hunting

Robin Briggs, Witches and Neighbours

Norman Cohn, Europe's Inner Demons

Owen Davies, Witchcraft, Magic and Culture 1736-1951

Carlo Ginzburg, Deciphering the Witch's Sabbath

Richard Kiekhefer, Medieval Magic

Brian Levak, The Witch Hunt in Early Modern Europe