The Rule of Thirds has been used for centuries by painters and photographers, and is important to remember when trying to get a well balanced shot. This rule says that an image should be divided into nine equal parts and that important compositional elements should be placed where they intersect.  Basically, the subject is placed off balance, rather than in the middle of the frame, at an intersection of one of the gridlines. Mentally lay this grid over your image through your viewfinder and try to place the points of interest in your shot along at the intersections. Or, crop photos after a shot and try to line up the points of interest then.

Rule of Thirds Gridlines

Tree Placed at Intersection of Gridlines

Here are some a couple great articles about the Rule of Thirds that provide a lot of photos as examples:

• Pro Tip: Rule of Thirds
• Guidelines for Better Photographic Composition: Rule of Thirds