Some of your photographs have the potential to look interesting with many different crops. Of course cropping reduces the resolution of your image, makes the noise more visible and reduce sharpness so you have to judge for yourself how much your are willing to crop.
Some photographers take pride in claiming that they never crop in post processing because they perfectly frame their shoot. In my opinion there is no shame in cropping an image, and the viewer of a photograph does not care. It is even a creative exercise that improves your abilities to see, frame and balance your photos.
For this article, I made the experiment with a photograph that I took of the singer songwriter Doctor Robert. There you can see how many variations are possible from a single image, and I invite you to experiment the same with your images. So here is the original image :
Crop for different formats
The first reason why you may crop is to produce different formats of the same element of the image. Your client may have need for square, 3:2, 16:9 or any intermediate ratio. The square format my be used on Instagram, for a Facebook profile pictures or for an album cover. A odd format of 851p x 315 is appropriate for a Facebook cover photo. Besides the practical need for a certain aspect ratio, they also produce a different feel.
Crop for different details
Cropping is also useful to emphasize different details of the pictures.
Tilting for dynamism or stability
Tilting is another powerful cropping technique. But be cautious with it since it make the picture more difficult to read by a viewer, it can even procure a sense of discomfort and to exaggerate I would say a sensation of nausea. I have seen some photographers systematically tilting most of their pictures, with the belief that a tilted picture is more interesting that a “boring” straight one. Unfortunately there is no such magic… A tilted picture may conveys more dynamism and a straight one is perceived as more peaceful or stable, but this only works with an appropriate composition, subject and mood. With this particular picture of Dr Robert, tilting is not so relevant, but for the sake of the experiment I had to show you some attempt at it :
I can only recommend you to play with the crop tool of your editing software. Play with rotation, aspect ratio, selective cropping and let you surprise by the results. After a while you’ll develop a better eye for composition and will be able to compose better directly in camera.