One of the things I like to play with especially when the light is not all that great is creating motion blurs. I do this by intentionally dragging the shutter (shooting at a slow shutter speed) when shooting a moving subject. What this does is allows any subject movement to register as a blur in the final image. This not only gives the image a nice sense of movement but it also lends a beautiful painterly effect to the shot.
How slow the shutter speed needs to be is really up to you, and how much motion you want to have. Obviously the slower the movement the longer the shutter will need to be open to show that movement. As a general rule when I am shooting a living creature I seem to like the eye to be reasonably sharp. because that is the first thing the viewer is going to look at and I just think it works better. For this shot of the elk I chose a shutter speed of 1/40th of a second. I was also panning with the elk as it ran by. By panning as I shot this, I was also able to blur the other background and foreground elements in the image which adds to the feeling of motion. Also, panning with the subject as it runs by helps to keep the eye and face relatively sharp.
If I would have had my camera locked down and made the image as the elk ran through the frame without panning, then the background and foreground would have been sharp and the entire elk would have appeared as a streak moving through the frame. Nothing wrong with that, just a different look and a completely different feel.
You can try this technique on any moving object, race cars, flying birds, blowing leaves, it is also very effective with moving water. Try different shutter speeds to see how it affects the image. Try some while panning with the movement and some without. Experiment, have fun, remember its digital so it costs you nothing to try. Also remember its digital so you can check your results on the back of your camera, you can look and see if you are getting the amount of movement you want.
Good Luck and Good Light!
Image: Bull Elk Running, Yellowstone National Park, WY