Here is a little cottontail I photographed in a field in a field near the Trinity River Audubon Center here in Dallas.  Slow shutter speed, pan with the subject, and don’t be afraid to fail – most of these types of images don’t work out, but if you stay at it you can get some that do.  With moving subjects that have wings or legs is to only blur them a bit (here 1/15 second).  Otherwise the legs would completely disappear and it would be a legless  hover-rabbit.  The other key is to get some semblance of a sharp eye.

Cottontail rabbit runningCanon 1D Mk III.  500mm.  ISO 800.  f/20 @ 1/15 second.