When I photograph people without flash or studio lights, which I do most often, I operate in a shutter priority mode. Even though I set my 1D X to manual mode with auto ISO, I typically fix the aperture to the widest setting that my lens allows (the lowest f-number), and adjust the shutter speed to freeze action. For sports, I usually start with a shutter speed of 1/1000 sec, and sometimes lower it to 1/800 or even 1/650, if the lighting is too dim.
Actually, depending on the lens (wider lenses can tolerate slower shutter speeds for the same subject), I sometimes obtain reasonable results while shooting sports with really slow shutter speeds, e.g. 1/125 sec. I should mention that I usually do not do this on purpose. Sometimes, I just forget to change the setting after shooting a relatively stationary subject and continue to shoot action, only to find out that among mostly blurry images, there a couple of nice ones. The benefit of the slower shutter speed is, of course, lower ISO and, therefore, less noise.
Of course, I am talking about freezing the motion, which is just one way to photograph action. There amy other way to convey speed, such as blurring or panning. “Understanding Shutter Speed” is a good overview book on this subject.
I was also happy to discover a shutter priority mode in the Camera+ app on my iPhone. Now I can can set the ISO to “Auto” and set the shutter speed to a reasonable value (around 1/60 sec) when photographing my daughter. The default setting of 1/30 sec is way to slow to capture a 3-year-old in her continuous motion. Incidentally, because kids are constantly moving, I find the fully manual mode of the iPhone Camera+ app (where shutter speed, aperture and ISO are all controlled separately) too cumbersome to use for spontaneous children’s portraits. While some control of the exposure mode and focus are nice to have, the point-and-shoot aspect is what makes the iPhone useful to me as a pocket camera.