Should you crop your photos? The short answer is... It depends. If you are a photojournalist then you should not crop your photos. Photojournalists generally do not make any adjustments to their photos because their clients (newspapers, local news tv etc) require that the photos be untouched for authentic reporting purposes.
If you are not a photojournalist then CROP the photo if it is needed. I attempt to get everything correct in camera because when you crop you lose image quality and besides, it is my job as the photographer to compose the image properly. This cannot always be accomplished so when cropping is necessary I do it without remorse or hesitation. When you are not taking a photojournalist approach the end result is the most important part of the process. If you photographed a crooked image then straighten it with the crop tool. If you see some weird person stupidly standing in the frame and you can crop them out then crop them out. While you are processing and you see that you can use the crop tool to tighten down on the image to really bring out the rule of thirds then crop…
The small example I have here is of a hockey player. The photo I took was originally a horizontal shot and it works on it's own (see the image at the top of this post). I have left plenty of room to the left of the player so it looks like he has a place to go and he is in the upper right third of the photograph. It is a sound composition. However, after talking with the team photographer of the Tampa Bay Lightning I found out that single images of hockey players are usually cropped horizontal. So, taking the word of a seasoned professional I made it a horizontal. And, well.... turns out he's right.
First and foremost get it as right as you possibly can in camera but always remember… You are an artist so use the tools that are available to make the best possible image for you and for your clients.