If you want a depiction of a classic, fairy-tale witch look no further than Book 3 of Spenser's Faerie Queene. The unnamed witch in this book, who torments Florimell in a number of ways, is your ugly, old, magical, conniving, forest-hut-dwelling witch-figure.
Her role in the text is primarily important because she creates the false Florimell for her lustful son to enjoy, and because the beast of lust that she summons chases poor Florimell all the way to the ocean. Historically, however, it's important to remember that witchcraft was considered a very real thing practiced by worshippers of the devils. A few hundred years before Spenser, witches had been systematically burned at the stake across Europe.
So while we might view your average witch as a typical convention of a good fairy tale, she embodies a much deeper, and rather disturbing, anxiety that played a large part in sixteenth century society and religion.