Can Cats and Dogs be Friends?

This saying reflects the commonly-held belief that dogs and cats just can't get along because they are natural enemies. People who share their homes with both species, or who have read The Incredible Journey, know that this is not true. Dogs and cats can form fast friendships. It is life experiences with members of the other species, and not an inborn animosity, that determines how cats and dogs feel about each other.

The initial meeting sets the stage for future considerations in the dog/cat relationship. Both species communicate with body language and, because they "speak" differently, misinterpretations may start the relationship on the right or wrong paw, depending on who says what to whom!
Personality types—and their tails
It is life experiences with members of the other species, and not an inborn animosity, that determines how cats and dogs feel about each other.

A confident, pushy dog will approach another with tail held high. This "go ahead, make my day" type of challenge is most often met with submission and/or appeasement from the other dog, unless the other dog rises to the challenge and presents a confrontational stance himself. A friendly, confident cat will approach with tail held high, also. This cat is saying "Hey, let's be friends."

Consider the situation when the confident, friendly cat marches up to the easygoing or submissive dog, tail flying high, head in the air, and with a confident step. The dog, not wanting any trouble, offers a polite greeting or backs off to see what the cat wants to do next. Either response is reinforcing for the cat; he learns that this approach to a dog works well. This type of cat will make friends easily with most dogs, because dogs misinterpret the friendly tail flag and are careful not to cause offense on the first meeting.
dog and cat playing

We have a dog-loving cat that uses this technique with any and all dogs. He even goes out onto the road to accost strange dogs walking by. The dogs are so taken aback that never once has our cat been chased. A visit from our neighbor's Great Dane was cut short when the cat marched up to say hello and the very timid neighbor-dog ran home at top speed with her tail between her legs. It is not so much a matter of size, but more a matter of how you walk the walk and talk the talk in the animal world.

On the other hand, the rare dog that does seek confrontation may react to the friendly cat by escalating the challenge. He may put his paw or chin on the cat's back or stand very tall and growl at the cat. This will frighten the cat, and the cat will run away—or stand and fight. Either way, this dog will have an entirely different impression of cats than the dog who just wants to get along.
Source: http://clickertraining.com