Composition can really make or break a photograph and I tend to keep these general "rules" and ideas in the back of my mind whenever I'm setting up a shot.
1. The "rule of thirds"
Imagine there is a grid that splits the image into thirds both horizontally and vertically and place your subject on either the lines themselves or the point where they intersect.
The theory behind the rule of thirds is that if you place points of interest in the intersections or along the lines your photo becomes more balanced and helps a viewer of the image interact with it more naturally. Apparently "studies have shown that when viewing images that people’s eyes usually go to one of the intersection points most naturally rather than the center of the shot." (see DPS)
If you need some extra help composing your shot, most DSLRs have the option to place a grid over your LCD screen as well as when you look through your viewfinder.
2. Follow the lines
Your eyes will naturally follow lines created in any scene. By thinking about where your eye is drawn and capturing those lines, whether they are set up vertically, horizontally or otherwise, you can help draw attention and pull the viewer into your photo.
3. Find a fresh perspective
Before taking a picture take the time to think about where you will shoot it from. Your viewpoint has a huge impact on the composition of your photo, and it can greatly affect the message that the shot conveys. Shoot from above, shoot from down low. The important thing is to try different set ups to help your photos look and feel fresh.
4. Fill the frame
I love to fill the entire frame of a photograph. By removing a traditional background you can create really great depth in your image and make your subject really stand out.