There are several ways to express motion in your photos ranging from freezing the motion with a very fast shutter speed to panning along with your subject using a slower shutter speed. You can also express a feeling of motion by slowing down your shutter speed to intentionally blur your subject.
One of the most exciting ways to portray movement in a photograph is to allow a moving object to become blurred. This approximates the way that our eyes perceive a fast-moving object. To record a moving subject as a blur, you must use your camera’s shutter priority mode to set a slow shutter speed, but the exact slowness depends on several factors, such as the speed of the subject.
These two photographs were taken at la Tour Eiffel, I cannot remember exactly the setting of my camera I only remember what I did was I made a quick turning of my 18-200mm lens while aiming at the subject of my photograph and clicked.
(source: How-To: Capturing Action & Motion)