If specific proportions for a certain end use are not an issue, then any cropping I do will be to increase the visual impact of an image. I might crop for any of the following compositional reasons:
1) To trim out distractions at the edges. If a little bit of something extraneous is intruding into the frame, then I'll crop it out. The exception would be if cropping would eat into something necessary, in which case I'll just clone out the intruding bit instead.
2) To trim out 'dead space'. If there is an area that doesn't add a whole lot of visual interest to an image, I'll crop it off to keep the eye from wandering into a boring zone.
3) To give the subject more presence in the frame. If I feel that the subject of my photo is getting a bit lost in the frame, I'll crop in on it to bring it 'closer'. Sometimes this means letting go of some interesting areas around the edges, but very often the old adage is true: less is more.
There are a few other compositional reasons why I might crop an image, but these are the three main ones.