In most portrait photos, the subject's eyes look directly into the camera. Have your subject express a variety of emotions to capture a unique photograph. You could also try to have the people in the picture look at something in the frame.
To avoid red eyes in your photographs, make sure that your camera either has built in red eye reduction or you change the direction of your flash. If you did shoot a photo and it contains red eyes, you can easily remove them through the use of a graphics software such as Corel or Photoshop.
Make sure to set up your compositions so that vertical lines are truly vertical. Tilting the camera backwards to capture a tall building, for example, can cause the building to appear as if it is falling backwards out of the frame. Photographs in which buildings are not vertical often appear unnatural.