Photography is non-verbal communication. One major key to creating successful photographs is to communicate with the viewer as clearly as possible. If the photograph is stating unnecessary words or seems to be communicating more than one theme, it will leave the viewer confused and unimpressed.
Often the simplest photographs are the best photographs. That's because the message of the image is stated as clearly as possible, with nothing unnecessary included. Generally (but not always) that is the best approach to photography: simple, straight-forward images.
You want to, as much as possible, crop your photographs before pushing the shutter release button. In the field, carefully consider how you want the final print to look. If there is something in the frame that does not make the image stronger, then remove it from the frame before taking the picture. Move a little left or right, up or down, step forward, step back, zoom--remove it somehow.
It is better to get the photograph the way you want it when you take it than to try and fix it later with computer software.
After the image has been captured, there are three general reasons to crop a photograph.
First, you might not have noticed something when you were in the field that is very obvious to you now as you look at the image on your computer screen. This happens when you are in a hurry--sometimes you have to be in a hurry, especially with quickly changing environments or fast-moving objects--and are typically found at the edges of the frame.
When you find things in your images that you didn't expect and don't want, crop them out! Get rid of them and make your photographs stronger.
The second reason to crop is to shape the image. Print shapes are not typically the same shapes as camera sensors. Decide what size the images will be printed. I consider this when I'm in the field taking photographs, so that I can compose the images in such a way that they can be cropped to that shape without losing anything important.
Once you've decided what size print you will make, crop the image to that shape so that you have complete control of how the photograph will look. Don't leave it up to the lab to do the cropping, because four out of five times they will get it wrong.
And even if you have no intention of printing the image, often one shape will create a stronger photograph over another shape. The only correct shape for a photograph is the one that is the strongest. Sometimes that shape is a square, other times a rectangle, and other times a long rectangle.
The final reason to crop is to zoom. Sometimes you will not have a telephoto lens that is long enough or a macro lens that will focus close enough to capture the image you want. Other times you simply didn't choose the best focal length, which typically happens when you are in a hurry (again, sometimes you have no choice but to hurry).
If cropping the image (removing unnecessary parts) makes the photograph stronger, do not hesitate to crop. There is no shame in cropping. Photographers have been cropping images for well over 100 years.
In conclusion, keep your photographs as simple as possible to communicate as clearly as possible. Crop out whatever is unnecessary. It's best to do that in the field before taking the picture, but by all means do so in post-processing if you didn't get it correct when you pressed the shutter release button.
Simple is better, but don't make your photographs uninteresting. Making complexity out of simplicity is very difficult. You have to find a way to inject thought and emotion into that simple subject.