Okay, so dogs don't really pee facing south. But according to researchers, who watched dogs pee 5,582 times and watched dogs poo 1,893 times, dogs have a strong preference for orienting themselves along the north/south axis when they do their dirty, shameful business.
Some variation was found in the urination orientations of male vs. female dogs, but the scientists posited that the wayward squirts might be due to the male dogs' tendency to lift one rear leg or the other (but never both!) during the act. This theory is supported by feculent evidence: male and female dogs assume the same, dignified squat when pooping, and show no difference in their defecation orientations
Alas, due to their small sample size (relative to dog subjects, not to the number of poops and peeps observed - they really went above and beyond there) the authors were unable to draw any conclusions about breed differences. Can Chihuahuas pull this off, despite their tiny bodies? Can Mastiffs feel the compass points, or is the gravitational pull of their own mass enough to throw them off? Further study is needed. You should be taking notes, PhD candidates!
I know I am making light, but this research did have a fascinating and important finding: dogs are sensitive to small variations of the Earth’s magnetic field. As the authors of the paper say, "In this study, we provide the first clear and simply measurable evidence for influence of geomagnetic field variations on mammal behavior." That's a pretty big deal! And who knows, if you and your dog are lost someday, it just might save you life. As long as your dog has to go, of course.