Um, I'm a Hedge Witch and I own a cat - Honestly!
Seriously, a witch is a person who practises some variant of pagan religion.
For my part, as a Hedge Witch, I tend to shy away from "organised" paganism, such a Wicca for instance, and seek my own road. There are rituals that are carried out on the great Festivals during the turning of the Wheel of the Year, but I think you'll find that most pagans don't tend to cast spells (unless they *really* know what they're doing or are incredibly stupid).
During the Dark Ages and the Early Medieval period many village wise women were accused of being witches as the Christian church was on the rise and were desperate to put an end to any free thinking by such women. The Church had to be the only recourse to the people in times of illness, despair, famine, etc. Most of the women who were driven out, or indeed, killed, during these purges were nothing more than midwives and herbalists but were seen by the Church as tempting people away from the power of God and therefore had to be exterminated.
Also remember that within the native pagan religions of the Celts and Saxons, women were accorded equal status with men and, in some cases, tribal heirarchy were matriarchal. Women's sexuality and power was celebrated in these religions. This was also against the teachings of the Church (see : Original Sin - women were to be put down and kept under control or their wanton sexual nature may pull godfearing men down into sin with them (duh!)).
Consequently, these women were branded as heretics and witches and persecuted. It is this persecution, and not so much the witch trials of the 15th/16th/17th Centuries, that has come down to us as the legends of witches and spellcraft.