Notes On Photography: Photographic images are often cropped to improve or to re-orientate the composition...
Do you crop your images? Yes, I do. First and foremost, when I am stuck with only a body, an un-idle prime, and a vantage point that is not at the best to my discretion. I will continue shooting, I will capture the event first, and work towards achieving the spectacular I was visualizing with cropping at post-processing.
Images are often cropped to improve the composition, to re-orientate and bring focus to the main subject, to zoom in on the subject that may be within the scope of a largely wasted space, and to change the orientation and the aspect ratio of the image. Cropping to a square format does suggest stability and formality.
One obvious reason to crop an image is to place more emphasis on the subject of the image. You may want to remove untidy elements that may otherwise spoil the intent of the image. Try applying the Rule of Thirds to the image you are editing, if you are not too happy with the visual impact of the image, try cropping it to the rule.
Cropping can also give an image a greater impact - panoramic vistas that may be too tall if shown in full, or vertical slits that may be the opposite if shown in full width. You may also crop your images to unusual shapes, not really recommended though. Try cropping an image to a circular shape and see what you make of it.
Cropping can also bring out emotion in you. The closer you crop to the face of a person, for example, the more personal the image becomes. A full-figure shot seems always formal, professional, and somewhat distant. Going for a head and shoulder shot, on the other hand, is friendlier and more intimate. Try cropping it closer.
Cropping can also be done to tell a story or context, to the extent that sometimes it completely destroys or completely alters the meaning of the image. There is always a limit on things that you can do - will cropping the image change or completely alter the story? Can it still deliver the message, or will it just end up being a pointless banner head image?