Space To The Left Or Right
If you photograph a person who's looking off in one direction, generally, you should position them to one side of your shot so their head is pointing in the direction they're looking. This makes the shot more compositional pleasing and it also helps guide the viewer's eye through the image, in the direction your subject is looking.
The same rule can be applied to moving objects too as the eye will naturally follow the path the subject's on and having no space for them to move into can leave the shot unbalanced. The space also gives the viewer chance to wonder what's outside of the frame and where the subject will be headed next.
Exceptions to the rules:
If you crop in close, not giving your subject any looking space, it can create a more moody image. Your viewer will also be left wondering what your subject is looking at which can help them begin to create their own stories about the shot.
If what's happening behind them will enhance the sense of excitement/action use it and ignore the usual 'space to move in to' rule. For example, a bike or rally car coming around a bend on a dirt road will leave a cloud of dust and dirt behind them that will add interest and create a sense of speed in the shot.
By positioning a person or animal who's running or walking to the edge of the frame (in the direction they're moving) you'll give the impression your subject is moving at speed as it will look like you couldn't keep pace with them.
Tell A Story About Their Journey
If what's behind/to the side of them is more interesting than what's coming use it. It can also help emphasis distance, for example, you may want to show how your subject's walked/ran a particularly long way. As with cutting out looking space in portraits, removing the 'action space' will give the viewer chance to use their imagination as they begin to wonder where the subject is going and what will happen next on their journey.
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