This all started when I left a comment on ant photographer extraordinaire Alex Wild's Myrmecos Blog to note that a large starting image file is good when one needs to crop the image so that enough pixels will be left to print a decent-sized final image at 300 dpi. Alex responded with this post, to explain that cropping should not be used to increase "magnification"; better image quality would be obtained by taking a more magnified picture either by moving closer to the object or by using a better lens. I agree with him wholeheartedly.
But sometimes cropping is a good thing. Here is a picture of the land snail Helix aspersa (= Cornu aspersum). This is the original uncropped image.
When I took this picture the snail was in my left hand and the camera in my right hand. Perhaps I should have moved in a little bit closer with the camera, but I didn't want to leave out any part, especially the tentacles, of the snail, which was continuously moving its head around, and at the same time, I wanted to include my fingers as a scale. So when I sold this picture to a photo agency, I cropped out quite a bit of the background. Here is the final image that will be printed in a biology textbook.
At 300 dpi, its dimensions were 16.6x13 cm (6.5x5.1 inches). I doubt they will print it that large; they may crop it some more or reduce the size. In this case, if I had moved in closer, I would have cropped less, but I doubt the final image quality would have been noticeably better.
On the other hand, if you are photographing something long and narrow, like a this slug Limax maximus, and if you want to include the entire animal in the picture there is a limit to how close you can get to it. In that case, you must crop.
Here is the uncropped image of the slug.
I could have approached it a little bit more, but not much, especially if it had had its tentacles out. The extra spaces on top and on the bottom are inevitable. So, if I wanted to print this picture in an article, I would do quite a bit of cropping.
Because I took the original with my 8 MB Olympus E-500, the cropped image retained enough pixels for a 21.7x5.6 cm (8.6x2.2 inches) print at 300 dpi. This is when megapixel cameras are indispensable.
Cropping a poor image won't make it better, but cropping a good image can improve it. Therefore, the rule of thumb is: if it's crap, don't crop.