The reason black cats are considered bad luck (or at least one of the reasons) is because witches like to keep cats around. Cats can see auras better than people, and auras are needed for any spell. Actually, it's not just black cats that should be feared. Witches didn't just own black cats. If you truly are superstitious, you should be afraid of all cats.
When I say witches, I don't mean the fairy tale witches with warts and broom sticks; I mean legit witches. I personally don't think witches or spells are bad... But as everyone knows, in about 1480 - 1750, people were scared of witches and they would go on witch-hunts to try and kill them.
That fear and uncertainty of witches was passed on through the generations and because the cats are associated with witches, they were considered bad luck because if a black cat is near by, a witch must be, too.
If you are the one who owns the cat, you have nothing to worry about.