I realize that cameras are different in their ways of autofocusing. My Canon 7D has an autofocus style called Zone AF which I most often use for sports and action photography. This divides the autofocus points into groups. I normally will select the top group of four points because I want the heads/faces of my subjects to be in focus...
I can select any group of points by using the controller joystick. However one nice thing about the 7D is that when I have the top group selected in the landscape or vertical format, it automatically switches to the top group when I move the camera to the other configuration. This keeps the area of focus most often on the heads of the subjects...
This works quite well both for large subjects like horses and riders
Using creative focus is a double edged sword. When using a wide aperture, the background is cast OOF separating the subject from that background. However, sometimes, you need an extra bit of DOF because you want the entire subject in focus. I shot the polo image at f/4 using a 300mm lens and was able to capture the image because the horse and rider were racing at a 3/4 view rather than a front-on view.. The horses head and the rider are in focus while the rear of the horse is just beginning to lose focus and the background is pretty well blurred...
The Zone AF also works well on smaller subjects such as this dog. I nailed the head and ball with Zone AF
I shoot in high speed burst mode in Servo-AF (continuous focus).
I also shoot using at least ISO 200 and often ISO 320 or higher to get the shutter speed I need. I'd rather have a sharp image with a bit of noise than a fuzzy image without noise...
I will also select the AF mode in which the lens doesn't focus to the closest point possible, rather has a limited focus range. This will achieve faster focus than if the lens needed to travel the entire focusing distance from close-up to distance...
I am fairly certain that most cameras have some type of autofocus and burst modes that work well for fast moving subjects.