The rule...
 

Shed some light on this matter:

http://www.palmettobayinc.com/PhotoT...ls/thirds.html

In other words simplify it.

Mentally divide the horizontal and vertical sides of the frame into thirds, breaking up the image into a grid of 9 rectangles. Place the most important visual elements of your picture at the intersections. As an example, in a close shot of a person or in a still portrait the subject's eyes are usually the most important feature. Let's say you're going to photograph this person in a quarter-profile with the right-hand side of their face to the camera and facing 30 degrees to the right of the camera. Compose the image so their on-side eye is on the intersection of the top horizontal dividing line and the left vertical dividing line and they're looking toward centre frame. If you're shooting an exterior or scenic, align the horizon line with one of the horizontal lines, not the middle of the frame. Shooting a long establishing shot of a lone figure in the landscape staring off at some distant mountains? Compose the shot so the horizon is on one of the horizontal dividing lines and the small figure is situated at one of the intersections of the horizintal and vertical divisions. If you wanted to emphasize the idea of the figure alone on the prairie, you might put the horizon on the top horizontal line and the figure on the intersection of the bottom horizontal and the left vertical.

in other words, for the most part and generally speaking (there-thats the disclaimer as there are always going to be exceptions) never set the primary subject matter dead center in the viewfinder. The is true be it still photography or moving pictures of any kind. It is far more interesting to the eye if the main subject is slighty (at least) off center. Even if you look at a magazine cover-say a fashion mag-you might think the subject is centered-it might be-but the model herself is not straight-IOW-shes got the model "C" or reverse "C" going. So it appears shes not centered. Even a well done landscape photograph-say an Ansel Adams type of the southwest US-the main feature of his print is off center. The list goes on and on.
NOW having said that there are times that centered is fine and acceptable. A speaker at an awards dinner might look better is centered-the CEO doing a message to the sales force might be better center-a bride and groom standing on the altar might be better centered. BUT for the most part slightly off center works better (I've been slightly off center my whole life-not sure if good or bad)
HTHs
Don

Auto focus vs. Rule of Thirds
 

I could be wrong, but I don't think the auto-focus systems of video cameras can follow the Rule of Thirds. They tend to focus on the center of the frame. Does anyone know for sure? I normally auto-focus (or Push focus if usuing manual mode) on the center of the frame, lock the focus manually, and then recompose the shot with the subject slightly off center.

(I think some Sony consumer camcorders with the touch screens let you tap the area you want in focus with a stylus. That would be a cool trick.)

you're right on that.

It is basically the rule of the golden section (get your maths knowledge out and think Fibonacci rabbits). It's one of the fundamental rules of Renaissance art and all art after it. It creates a well balanced image. You can have great fun looking at Rafael's School of Athens for example and find all the math in it :-)