Don't center the subject!
OK, the composition police aren't going to come knocking on your door should you break the rule, but it's a good guideline.
See, when most people shoot an image, they stick the subject smack dab in the center. Yawn.
Sure, sometimes it can't be avoided—maybe you have a subject that fills the frame and centered is really the only way to go. You may also run across a composition where anything but centered wouldn't look right. It happens, but not usually.
I've found that at least 90% of the time I can get a better image by moving the subject off center. Just how much off center—and in what direction—is the trick :-)
There is a compositional rule known as the "Rule Of Thirds". Basically, it says to mentally take your viewfinder and divide it up into thirds—both horizontal and vertical. Where the lines intersect are the "power spots" (say that with a deep booming voice and an echo for the full effect). Try to put your subjects as close as you can to the intersections.
Here's an example of how this works. The frog is right on one of the intersections
Even if the subject doesn't look right placed smack dab at an intersection, try to keep it along on one of the lines. For example, if you have a landscape photo, try keeping the horizon either on the top or bottom line—don't run it right through the center of the image.
In my experience, this technique is a solid foundation for composition. It's where I start every time I look though the viewfinder. In fact, once you do it long enough, you'll find your compositions will become as much instinct as thought. You'll simply wiggle the scene around in the viewfinder until the comp feels right.
For example, in this shot the lady bug is close to an intersection and lies along one of the lines. It's not exactly on the mark, but this is generally what happens. You try it various ways, and end up close to an intersection or line.
Another cool "Rule of Thirds" trick is to try to string your subject from one third of the frame to the opposite third. It gives it a nice flow and is almost a guarantee of a powerful image. You can usually do this just by changing camera position
I know, you may not like snakes all that well, but look at how, from the head down, it flows along the grid lines. I started with his head (or her head, I didn't check) close to an intersection and moved the camera until I had the composition I wanted:
Here's the same effect with a waterfall. The main part sits in the top left third, then flows to the bottom right third:
OK, I want to stress that the Rule of Thirds isn't a hard and fast rule. I break it all the time. Sometimes elements in the photo simply don't lend themselves to a textbook "Rule of Thirds" composition. So, I fiddle around with it as much as possible. Bottom line: use it for a starting point and then adjust as needed. If you're shooting digital, taking the picture is free, so try it several ways.
Finally, when using the rule of thirds, pay careful attention to the rest of the image. You may find that you need to change the camera position to make the composition balance better. Just sticking a subject on a random intersection doesn't guarantee a great photo (a lesson I learned when I first started shooting).
In this last example, the waterfall not only sits on a line, but on two intersections. It was good, but not overly interesting until I found a tree for added interest. So, I moved around until I had the composition below. The waterfall is the main subject, but it's not just hanging out there, all unbalanced.
The trick is to use everything in the photo to add to the composition. Try all 4 intersections - you'll probably find that one will jump out at ya!
Give it a try, have fun, and watch how much more powerful your images are.
(by the way I didn't write that lol)