Progressively increasing the shutter speed gradually decreases the blurring of your subject’s motion, and beyond a certain threshold its movement becomes practically imperceptible—the action is frozen in place. This idea of “practically imperceptible” motion is analogous to the concept of acceptable sharpness (see Depth of Field): it depends on the resolution of your camera, but more importantly, on the degree of photo enlargement, cropping, and the intended viewing distance.
The surest and most accessible  method for freezing movement in photography is by using the fastest shutter speed your camera can achieve, which for most modern interchangeable lens cameras falls into the range of 1/4000–1/8000 second. However, this technique is only sensible under bright sunlight, and would otherwise require fast lenses, increased ISO, or both (see Reciprocity Law). In practice, photographers tend to shoot at the slowest shutter speed that freezes the action of the subject in their viewfinder (keeping in mind an appropriate aperture). Although a shutter speed of 1/4000 second will dependably freeze most action, it’s arguably excessive for portraits, architecture, and landscape images, and requires exposure compromises that may otherwise be detrimental to overall image quality, leading to increased aberrations (due to large apertures) and image noise (due to high ISOs) if the scenes aren’t adequately bright.
Fast shutter speeds ranging from 1/500–1/8000 second are often appropriate (and necessary) for freezing the motion of dynamic and animated subjects, such as at sporting events (especially water-sports, due to the drops of water), athletic competitions, of birds in flight, airshow fly-bys, motorsports, and so on. With that said, it’s crucial to remember that the subject’s speed within the frame determines the shutter speed at which their movement becomes practically imperceptible.
Choosing the right shutter speed for freezing movement
There are several common sense techniques to help you select the slowest shutter speed that dependably freezes fast movement. Photograph your subjects using shutter priority mode—estimating the shutter speed you believe will freeze their motion—and check your results on the camera’s rear screen. Zoom into the photo and pay close attention to the fastest moving features of your subject, such as the tips of the extremities. If you notice distinct motion blurring, increase your shutter speed and try again. Once you’re satisfied with the results, confirm the exposure parameters, and mirror the settings in manual mode. As long as the light remains constant, shooting in manual mode will ensure that your exposures will stay consistent across multiple photos.
For every doubling in size of the subject in your viewfinder, select a shutter speed that is twice as fast. For example, if your quarter-frame photos of a pole vaulter reliably freeze her action at an exposure of 1/500 second, then, use a shutter speed of 1/1000 second for compositions in which her body fills half the frame. This compensates for the fact that increasing your subject’s magnification will proportionally increase the speed of their movement in the frame. In situations where you anticipate dynamic shot lengths, it’s more convenient to set your shutter speed to reliably freezes action at the highest foreseeable magnification.