I come to this question as a painter and could not agree more strongly with Jim Chinn. Content "impact" is great, but the point I tried to make in the thread on pictures of the year stands true here as well. You can make an unremarkable picture of a remarkable thing or event. It's hard to screw up the proverbial catch of the baby thrown from a burning building, I admit, but there are rules (not tricks) of composition that make any picture much stronger. They are rules of thumb - to be broken at will when something else trumps them but they are rules.
Some simple ones:
Watch the sweet spots (or "the rule of thirds") A viewers eye, in western culture, goes naturally the spots where the lines of a tic-tac-toe game drawn on the picture would converge - one third of the way from one edge to another, vertically and horizontally. Placing an important element in one of these spots gets it noticed more easily - especially if it is a subtle element.
Negative and positive space balance one another in an image. This has been talked about as the push and pull of foreground / background, the interplay of light and dark, the balance of being to emptiness... lots of things. All it means is that you should pay attention to the concept of balance in the image. Great emptiness can balance a small spot of energy in an image and make the whole thing work. This is the lesson the impressionist painters finally learned from Japanese and, eventually, Chinese images imported to Europe in the second half of the 19th century.
Imbalance can cause energy. Use it wisely.
Edges count. Hard edges draw our eye and act as pointers.
Vertical lines organize, horizontal lines quiet and diagonal lines energize. Think "Baroque."
The outside edges pull against the middle - most of all in a square composition, I think, but that's my take on it.
The more balanced and centered a picture is, the more "gravity" it has. Think religious, political or even corporate portraits. Also, the greater chance it has of being deadly dull if the content doesn't carry it.
There are more, but these are a sampling of what I mean. Using these ideas as organizational tools, great photographers have made wonderful images of eggs or leaves, kitchen tools or rocks. Are these images less impactful than a good picture of a war casualty? Of course they are, but they are not without their own strengths. Think of what a great photographer does with the rules of compositionand great content!
Thanks to everyone who have shared their experience. I particularly drew a lot from Jim Chinn and Whitey. Thanks again everyone.