Almost any breed of dog can be good with cats, especially if they are raised with them. Terriers (jack russells, airedales, fox terriers) and sighthounds (greyhounds, whippets, salukis) are more likely to chase and even kill cats, since these breeds were bred for hunting. Consider the cat's personality as well. A "dog savvy" cat is less likely to trigger a dog's prey instinct, but an aggressive cat can hurt a small dog.
Golden retrievers, like other retrieving breeds, have a natural tendency to be gentle and have "soft mouths," since they have been bred to retrieve game for hunters carefully without mangling it. Goldens have a well-deserved reputation as good family dogs, because they are rarely aggressive. Although a young golden may be boisterous and want to chase cats, it is less likely to harm them. A cat who calmly stands its ground instead of running away will defuse a dog's playful desire to chase it; a dog can't chase a cat that's sitting still.
Despite its impressive size (they can weigh over 100 lbs) the Great Pyrenees is calm and watchful over its "flock," including the family cat. Like most livestock guardian dogs, the Pyrenees is a faithful guardian and patient with the smallest animals, although it may try to repel strange cats, perceiving them as a threat. The American Kennel Club standard describes the Pyrenees as a tolerant and quiet dog with its family, but one who won't hesitate to defend its territory from intruders.
The bichon frise is a gentle, playful dog, and according to the American Kennel Club (AKC), "a cheerful attitude is the hallmark of the breed." The intelligent little bichon is bred as a companion dog. Since it's not much bigger than the average house cat, a bichon and a friendly cat can make good playmates, especially when raised together. When introducing a cat and a dog for the first time, give each space to investigate each other without undue stress by using crates or baby gates. A frightened or aggressive cat can lash out and scratch a dog and small dogs are especially vulnerable to cat claws.
Many dogs who are tolerant with children are also tolerant with cats and the boxer is no exception. A medium-sized dog with a long working history, including war time messenger dogs, property guardians and hunting, the modern boxer is primarily purchased as a family pet. They are especially gentle with children, and most are very good with cats.
Mixed breed dogs have temperaments as varied as their looks, and many mixed breed dogs can be very good with cats. Most dogs regardless of breed or breed mix, if well-trained and raised with cats, will be tolerant, if not affectionate, with the family cat. When adopting an adult dog, look for one that was raised with cats, or has been kept in a foster home with a cat. Bringing an already cat-tolerant dog into a cat-owning family is a lot easier than getting a strange dog and hoping that everything will work out OK.