Since I run a shelter, sometimes people ask me which dog breeds are the worst to have around a cat. The most "accurate" answer, of course, is that any dog can be dangerous to cats, depending on how the dog was raised and how it's treated now.
However, that said, it appears to be true that certain breeds do have an apparent propensity for what appears to be an inborn dislike for cats and one would therefore, be ill advised to keep one in the same home with a cat.
Those breeds are the pit bull terrier, the Jack Russell Terrier, and the greyhound.
Pit bulls, while gentle, sensitive and loyal to the family, for the most part, cannot be trusted to be alone with a smaller animal, or one that is subordinate. In other words, many "pits" seem drawn to attacking another animal that is lower in status or is much smaller. Possibly an instinct? I don't know.
Jack Russells, or "JRT's," also seem especially drawn to attack cats. That could be genetic as well. It just means that you should never leave your dog and cat alone together without supervision.
(By the way, I just heard that JRT's have been given a new name: Parson Russell Terriers.)
Now, the greyhound is included because, well, let's face it... they're bred specifically to chase a "rabbit" around a race track. How are they supposed to know your cat isn't "one of those?" They are large dogs with big teeth.
Just a note of caution here: Unless you're 100% certain your dog and cat are best friends, it's just not a good idea to leave them unsupervised when they have access to each other. Just use common sense. If you aren't comfortable leaving a dog alone with your infant, don't leave him alone with your cat, either.