There's a whole school of thought that says that Cartier-Bresson never cropped, so nobody else should either, so there!
You might just gather that I didn't go to that school, and whilst I do rate Monsieur C-B as a photographer, I also realise that he's one out of many talented people with a camera. But the blind "Do Not Crop" mentality isn't one adopted by all the others. Indeed, I don't think it really was C-B's intention to "Not Crop", even if he was clearly a man who could do in-camera composition through the viewfinder, on the fly, extremely well.
That's not to say that every picture you take needs a crop. If you are regularly chopping chunks out of all your images to "improve the composition" it's probably a good thing to step back a bit and ask yourself why? Because you shouldn't need to for many pictures; that's why we have viewfinders.
A small confession first - and it is something I am aware I do and try to watch for, not always successfully. I wear glasses, and I sometimes find my compositions being a bit off to one side in the odd picture. I've thought about it and tried to get a feel for what's happening and I reckon I'm not always lining up the spectacle lens just so on the viewfinder. There's sometimes a bit extra "space", nearly always on the right, than ideal. So sometimes I'm making a crop to get rid of this human error. Interestingly, it happens less with my D3's than with the company D300's, so I don't think the square Nikon viewfinder is as specs-friendly as the round one.
But mostly, I take the view that you should be sorting composition and framing in the camera as far as you can. This is my view for picture-taking generally. I came from film, especially slide film, and that meant getting things pretty right from the outset. Yes, digital means a variety of image editing programs available to us, but why add extra things to do after you put the camera down if you don't need to?
There are always exceptions to this - it's not another blind "Do Not Do This" edict. And just to muddy the waters a bit, I also don't believe any picture is "print-ready, straight from the camera", so all images should have some form of MILD tone adjustment done to them. But that's the key word - mild. You are optimising the look of the image, but you should have gone as far as you can to do so before you press the shutter, as that way you've got the best data to optimise.
It may be that the image you need is not 3 x 2 proportion (or whatever your camera shoots). If you need 5 x 4, square, 16 x 9, then by all means hit the crop button. But otherwise, if you have time to think, plan, and interact with your subject, then you should be aiming to include only what you want to see. If you always crop around a picture you've planned, then it's time to step closer or zoom in. As a newspaper snapper, I have to remember any newspaper's space for any picture is limited and that usually means every picture is tightly framed. There might be a post later about just what happens after your carefully tight-framed pictures are filed, though...
Action is probably the biggest compositional and cropping exception. If things are happening right in front of you then there's always the chance that it won't fall just so in the viewfinder. Then you need to decide if a bit of trimming will focus attention or improve the framing by cropping in. I can generally do composition on the fly, but it pays to leave myself a little bit of leeway. For example, in team sports, the peak action will rarely take place JUST so, as the players have the whole playing area to work inside. Then it's time to crop away some of the dead space around a tackle. Even here, you've got to be realistic and decide at what point you stop shooting as the players are just too far away. I'll be a bit more specific: From a 12mp D3, I will crop a really good upright action moment out of a view picture, if it uses the full height of the frame - that's still a 5.3mp final image at 3 x 2 proportions. However, I usually think very carefully about a picture if I have to crop it below 8mp. This is why news and sports photographers frequently use 2 (or more) cameras - long lens on one, shorter lens on another, and as the action gets closer they reach a swap-over point between bodies.
Even in action images, there's still merit in keeping the lens locked onto your subjects as they get ever closer - keep tracking, keep shooting, and you might be rewarded with a great moment that fills the frame.
No cropping required...
Here's a couple of soccer pictures - the first the uncropped one, shot on a D3, with a 300mm + 1.4x converter giving 420mm of lens. It's close to being too small, but it's a good clear action moment (rare this far down the league ladder...) and the background is also pretty clear (again, rare this far...) so I went with it:
And then the cropped version - I gritted my teeth and went to 6.0mp on a 5 x 4 proportion, though the filed version stayed at 3 x 2, as, technically I'm not supposed to do ANYTHING to my pictures (Shhhh, don't tell!). I could take it a bit tighter, but left the remaining space for the production side to do what they will.
And finally, here's one that is the full 4256 x 2832, uncropped. Ah, joy, it happens sometimes! Again, the sides could be trimmed but I left it as it was to file.