Last week I judged a number of entrants in a 7th grade science fair. The one I liked the best investigated a number of dogs to see which paw they favored. This depended on which hand the student held out. When he held out his left hand, all dogs offered up their right paw. But when he held out his right hand, half of the canines shook it with their left paw. I conclude from this that far more dogs are lefties than humans, who favor their right hand by a ratio of 9-to-1. Based on what I read here in the Washington Post and see published on the internet, my guess is that dogs are split 50/50 left versus right. The same may be true for cats, although they might be slightly more likely to right-pawed according a study noted in the Post article.
Just for fun, test your pet by putting a snack just barely within their reach. Which paw do they put out? Make a note. Do it again a number of times. If you see what seems to be a significant bias to left or right, let me know.