In the sixteenth century, witchcraft was certainly perceived to be a reality. People throughout society believed witchcraft existed and was being practiced to varying extents. That being said, how witchcraft was viewed is something entirely different. Views of magic and witchcraft throughout the Middle Ages and into the early modern period are anything but consistent. Even in the more "enlightened" period of the sixteenth century, some placed value in magic and witchcraft as worthwhile endeavors. Degrees of magical practice were seen as less problematic than others. Astrology and alchemy, while not always deemed the most appropriate activities, were typically seen as less of an issue than other forms of magic. Some magic (i.e. "black" magic), which sought to control human will, was perceived as evil, and this is generally where witchcraft falls in the early modern worldview.
The majority, however, and specifically those in the Church, handled the question of witchcraft very severely. The Church certainly believed witchcraft existed, and, guided by this belief, it actively pursued those thought to be witches, interrogated them to force them to confess their evil ways, and would even provide them the opportunity to recant. Generally, the view of witches and the punishment of them fell under very similar guidelines as those regarding heretics. If found guilty, the most common form of punishment was to be burned at the stake. Depending on the level of superstition, however, the punishment was more elaborate. In some cases, the witch's head was severed before the body was burned. Ultimately, the ferocity of the Church's attitude toward witches is very illustrative of its view of them, and by extension those of the general population.
Witchcraft was seen as a very believeable topic in Shakespeares time. If you were suspected of being a witch you were either drowned or burnt at the steak.