For me, just studying the works of other photographers that I admired, even if I was not interested in their respective genre, has proved instructive…I think. But this, in a sense, goes back to what Allen stated: deciphering and incorporating the visual grammar or language in the photos observed. And by doing so, it is not as simple as merely copying, but instead a matter of using this language to hone one's personal perception of balance, movement, and aesthetic expression.
There are a number of quick 'rules,' but, again, as Allen noted, style manifest when one's approach becomes effectively second nature, whereby applying or ignoring the rules is not so much a cognitive act but an engrained function of one's own visual judgment and preference.
Where it becomes even more complicated is that often various factors are at play, with, for example, lighting affecting the balance of shape. Meanwhile, shapes can complement or conflict with one another, and all of this interaction is having to occur within the confines of a deliberate frame.
A strong example is provided above, where, in mtimber's photo, 'burning' in the highlighted area helped place not only greater focus on the main subject, but also increased the sense of depth between the subject and background. Tonally, it is also more pleasing. Allen, I like it as is edited, so there! Actually, I understand your point about cropping it all out (and it certainly works that way), but to me, with it darkened, it adds a complementary, rather than competing, degree of 'space.'
This of course, brings up the fact that subjectivity is ever present, but if we want to retreat to "it's only an opinion," then there's really no need for any further discussion.
In addition to dissecting photos, I've also found it helpful to closely study other forms of art; I reckon even literature is not out of bounds...expressive flow is arguably transferable. It can all apply. I have a stronger background in music, and much of my philosophies on music have undoubtedly carried over to photography.
I know there are some folks on POTN who are more technically oriented and thus place greater emphasis on the technical aspects of photography. However, for the most part, unless doing documentation or reproduction, there is largely no escaping the "artsy" process of where to place the frame, and I can only guess that some of these folks might be underestimating there abilities to improve on this, fearing that they are just too left-brained.
Yet, when discussing "getting it right in the camera," composition is often lumped in as a prerequisite as though it were a technical procedure. Yet, composition has more to do with the aesthetics than with the technical (although one would hope to be technically inclined enough not to crop out there dear ma's head when taking a photo, unless making some type of statement, of course). Again, there are basic rules (ones that can be defined mathematically, therefor technically) that can help improve composition, but discretion evolved from some degree of visual fluency is ultimately what overtakes the yoke, giving form to personal style.
Proper exposure is a technical matter, but the use of light is not. How a studio photographer sets up his lights entails technical issues, but the overall effect also relies on artistic considerations.
Likewise, attaining color accuracy and white balance falls into the technical, but effective use of color transcends the technical, as demonstrated in the color photos of Ernst Hass (http://www.ernst-haas.com/index.html).
Just as an aside, there is no sin in cropping after the fact to improve composition, but it should also be remembered that one can't crop "in" something.
Anyway, I can only reiterate the value of studying and examining the artistic works of others, whether the works involve photography, painting, music, poetry, sculpture, and so forth.