Here is an interesting bit of scientific/artistic conjecture. Christopher W. Tyler, of the Smith-Kettlewell Eye Research Institute in San Francisco suggests in this short (1 page) illustrated article that a high percentage of portrait paintings are arranged so that one eye, presumably the dominant one, falls on the horizontal center line of the image, even when the head appears to be centered in the painting. (He goes into more detail in a second article.)
He cites a number of examples and invites speculation on the part of the reader as to the purposeful placement of eyes in portraits according to several artistic models. His results from a sampling of 282 different artists suggest that he is correct a large percentage of the time and my own casual observations seem to agree.
Get out your ruler and art books and see for yourself.
The site is part of the Smith-Kettlewell Brain Imaging Center, which also includes The Eye Page, with interesting tidbits about eyes, both human and those of other animals, and a series of Art Investigations, scientific inquires into various aspects of art.