Here are a few composition principles that I have found to be helpful. Click on the bold title to see a photo sample of that principle.

SIMPLICITY  -- Move in close -- eliminate anything that doesn't relate.
UNITY  -- Cohesion of elements (color, shape, subject matter, etc.)
BALANCE -- Distribution of  . weight. -- real or imaginary.
CONTRAST -- Dark and Light, colors, shapes, subject, etc.
DEPTH -- The perception of three dimensions -- using dark values in the background and light values in the foreground, or soft objects in the background and sharp objects in foreground, etc. 
PERSPECTIVE -- Using converging lines to give the illusion of distance.
FOREGROUND OBJECTS -- Objects placed in the foreground adds to the feeling of three dimensions, and a design that is unified.
LEADING LINES -- An object that points toward the subject is a leading line, whether it is an actual line or implied. 
"S" CURVES -- This traditional technique adds depth and grace to a photograph by gently leading the eye to the subject.
VALUE -- VALUE Contrasting values make a lively composition, while complementary values bring harmony. 
TEXTURE -- The illusion of texture makes a photograph seem almost tactile, and adds the impression of reality.
GEOMETRIC SHAPES -- My favorite, deliberate visual ploy.  Look for geometric shapes -- implied and real -- overlapping and separated -- especially triangles and circles. 
REPETITION -- Repeating a shape, theme, color, etc. can give a stable comforting image.
SEPARATION -- The subject should usually stand out from its surroundings 
RULE OF THIRDS -- If you divide a photo area into thirds from side to side and top to bottom, then place the subject at the intersection the imaginary lines at one side or the other, you will often have a more pleasing composition that placing the subject in the center (this is called the bulls-eye syndrome, and should be avoided most of the time).
VARIETY  -- Making the visual areas of a photograph different in size, width, shape, etc, can make for a more interesting composition than having them all the same.
BREAK THE RULES -- Rules are made to guide us, and can be broken if the impact justifies it.