I have a preference for action photography. In my job as a sports reporter for our local paper I'm often called upon to get shots of basketball and football games and I find it to be the most challenging but rewarding type of photography. It's usually a case of being in the right place at the right time and taking lots of shots which is easy to do with a digital camera. If you're using film you have to be a lot more selective in your shots and a lot more patient.
Most of all it begins with developing a feel for capturing the exact moment that tells a story. The picture of the kid dribbling down the court is fine, but capturing the exact moment when the winning shot is made is better. The running back captured at the moment of contact with the tackler, or the batter caught ripping that shot to left field is an image anyone can understand and translate to their own personal experience. Knowing your sport and developing your timing is something that comes with experience, but entering with the right preparation and knowledge is a good start.
It's also important to know about the participants in the sport you are shooting, especially if your shots are going to be used for publication. My editor is always looking for the shot of the hometown kid who scored 35 points, even if it's not as good a shot as the one I took of the opposing player who hit 40.
The equipment needed for action photography is not all that different from the equipment used in any other photography. I like a fast camera of course because the lighting conditions are not always ideal. A good flash is important in nighttime football games and indoor basketball. I also believe in shooting at several different shutter speeds because sometime the blurring effect of motion is more dramatic than the absolutely perfectly exposed shot that doesn't convey the sense of motion in the sport.
What I'm looking for in my photographs of a sport is the idea of an image that tells a story by itself. In the newspaper we use cut lines of course, but who needs a cut line if you can capture the face of the kid who just made the winning shot at the last second, or the faces of the players on the bench as they realize their season just came to an end?
Every picture tells a story, try and make it obvious what the story is.