There are good creative reasons for intentionally capturing motion blur in your subject. Motion blur happens when the shutter is not fast enough to give the appearance of stopping the motion.
Flowing water is the classic example. Depending on the water speed, anything slower than 1/8th of a second will start to give the water a silky appearance. The slower the shutter, the less detail is recorded in the water.
Wings of a bird, legs of a runner, and wheels on a car are all other good examples.
This is where experimentation pays off. Learn what works for you and your subject.
Combining camera motion with subject motion and a slow shutter can leed to some great creative effects.