As mentioned above, where a photograph is taken is just as important as when it is taken. Cats, for example, do not typically enjoy posing for the camera. It is best to photograph a cat while it is lazing in its favorite sleeping spots, such as a couch or the floor. Scatter the family around and start snapping. You may only get in a few shots before the cats grows disgusted and walks off. Remember that taking a great family photo is not a race. You can even use photographs from several different sessions and eventually find your favorite.
Dogs are much more social and more likely to want to be with the family during photograph time. Your biggest challenge may be in capturing the shot with all the movement. If your camera has a sports shot feature, turn it on and snap photos of the family playing with the dog. These candid shots can sometimes turn out much better than any posed shot ever could.
If your dog is trained, then it may be possible to use the down and stay commands to get the dog to stay in one spot. Position the family around the dog in a semi-circle facing the camera. Tallest child should be in back and shortest children closest to the camera.