Cropping a photograph can make a world of differnce in what you are trying to convey in your pictures. Not everyone is going to feel the same way about the photograph. Some will like it one way, while others another. Like fine art, everyone has a different taste. And photography is an art form that with the advent of digital photography and manipulation can be enjoyed by many people. It really doesn't matter if you have a inexpensive point and click or an expensive dSLR.
Depending on the subject matter, you may not want to crop anything at all.
Do you want the subject to be the center?
Do you want it to one side? perhaps giving a bit of dramatic effect?
Perhaps there is something else in the photography to focus on.
The key is... allow yourself to have fun with it. Let your imagination run wild. And when you hit save... do save as, so as not to overwrite your original picture. You may want to do something else with it.