Whether to shoot with the left eye...
Interesting. I remember many of my left-eyed friends would get poked in the right eye by the wind lever on various Nikon bodies sold through the '80's. Motorized film winding has more than just the obvious advantages.
As I understand it, eye preference is pretty well built into your brain's "firmware" in the same way that you're born right-handed, left-handed, or generally ambidextrous. You can train yourself to make the switch, as some of my friends had to do with their eyes, but it isn't always easy.
Sports photographers tell me that after a while they learn to shoot with both eyes open, as Antonio suggests, so they can see approaching action before it enters the viewfinder. I got to the point when shooting a series of American football games that I could almost do that, but I lost the skill when I my sports career mercifully dissipated.
Speaking of two-eyed viewing, I have a question about old cameras. At a flea market in London I once saw a press camera, manufactured in the fifties I'd say, which used a viewfinder system in which one eye looked through a finder lens and the other eye saw a wire frame. At least, I think that's how it was arranged. Anyway, the effect of the two combined views was to create what I thought was a nearly perfect viewing experience. It allowed for natural peripheral vision while the photographer's brain superimposed a very clear frame inside the view. Does this system sound familiar to anyone? I think Kalart made something like this, but I believe the camera I saw was an English 4x5. (Sorry, 5x4!)
My eye doctor tells me that people who are right-handed are generally right-eyed. But he mentioned a very interesting exception, which is that many great baseball hitters violate the trend. If you think about how a hitter stands you can understand how a right-handed hitter, for example, would want to favor the eye with the clearest view of the ball, his left. Even more interesting is this question, which he says is still unanswered: do great hitters develop the crossover, or does an existing crossover contribute to their great skill?
As for vertical shooting, a Nikon School instructor told my class many years ago that he shot, right-eyed I assume, with the shutter button side of the camera down, because that kept his hands and arms closer to his body and this gave him better stability. I dutifully followed that advice for a long time but finally gave up. The position is so uncomfortable to me that I think I create more instability by shaking. Yes, my right elbow is out where it shouldn't be, but now I'm a happier person.