When working with images of people, cropping doesn't mean 'chopping' out important bits of context or history. Rather, think of cropping as the act of cutting away unnecessary or unwanted portions of an image to help focus the viewers attention and help tell a story. Here are a few examples of reasons to crop:
Cropping can help to make the primary focus or center of attention clear. Typical snap shots often lack a focal point, as does this example. Cropping is used to remove unwanted and distracting elements such as the high-rise on the left and cars in the background. Cropping has also eliminated the lamppost coming out of the top of the child's head.
Consider how the viewer's eye moves across an image and allow for that movement. In a portrait of someone looking left to right, allowing space for them to look into brings meaning to the image. In this example, tight, centered cropping might not allow as much movement as a wider cropping would.
For Dynamic Effect
Rethinking the crop can serve to compliment the subject, help reinforce the composition and create a dynamic image. In this example, the original image is centered and ordinary. By cropping close on the face and using the rule of thirds, the tassel creates a strong vertical line and attention is drawn to the subject's eye.
Nearly any photo can be improved with good cropping.