Cats have a long tradition of being thought of as a psychic animal and in touch with the other worlds and so close to the Gods of old - usually they were seen in a very positive light, for example with the Ancient Egyptians.
However, coming forward in time to the 16th and 17th centuries in particular, when religious paranoia was rife against anyone who was a little bit different or didn't fit in, anything was used to state that they were involved in witchcraft. When they talk about witchcraft in these times, they are referring to people who worshipped the devil/Satan - in reality witches don't believe in Satan. When someone was accused of witchcraft 'evidence' of sorts was often produced - made up usually - that stated such and such a person took on the form of some kind of animal - usually a cat, hare or bird. These animals are referred to as 'familiars' and with the paranoid people these animals represented Satan/demons in disguise who took this form in order to assist the witch. The witch in turn, was also accused of turning her/himself into the form of an animal - again a hare, cat or bird being the usual forms.
However, in reality a 'familiar' is really a spirit guide or guardian spirit with no evil powers and no intent to harm. They are often not physical animals at all, but met through mental training and meditation. They assist, protect and guide people on their journeys into the other worlds. Shamans have animals guides as well similar to Wiccans. The black cat association with witches in art and stories probably comes from the folklore and history told about the witch trials, but the source might also go back further in time. As Halloween became more popular, then the witch and her black cat became a popular visual image of this time, but it's based on misunderstandings and ignorance. I think that a Wiccan or Shaman would be able to explain all this much better than I have, but I think I've put in the main ideas. Hope this helps a bit.