Here are a few shots I have so far that illustrate this concept.
The first two shots show a little blue heron: the first one centered withing the frame and the second one applying the Rule of Thirds. Personally, The second photo is a bit more interesting, although it would have been better if the lighting was better...the little heron blends in with the rocks a bit too much!
f/5.6
1/640
ISO-200
55mm focal length
AWB - Custom
f/6.3
1/640
ISO-200
55mm focal length
AWB - Custom
The next set of pictures all show some form of using the Rule of Thirds rather than centering the subject within the frame.
f/10
1/160
ISO-100
18mm focal length
AWB - Custom
In this one, the clown (subject) is to the far right of the image rather than centered.
f/13
1/400
ISO-100
55mm focal length
AWB - Custom
In this photo, there is more sky than water. I tried to take this shot so that the horizon line would not divide the photo into two equal parts.
f/10
1/200
ISO-100
43mm focal length
AWB - Custom
The sailboat (subject) was shot to take up the full frame from top to bottom, but was placed to the far right of the frame rather than center.