A conversation was sparked maybe a week or so ago by Journeyman at Japanese Jiu-Jitsu. The subject was training while blindfolded and it brought to mind an article I read a few months ago in a martial arts magazine (which one, I don't know). Anyway, the instructor was suggesting doing technique and even light sparring with one eye closed/covered, as it really throws off one's depth perception. The idea is to simulate an injury to an eye, or more likely, a cut near it that is impairing the vision. He suggests it becomes a much different game, using one eye, and could be a useful drill to hone balance and perhaps save your butt if the situation ever arose (he's likely referring more to ring and cage fighters, although I would think it could also have defensive implications).
If you try just to close one eye and do stuff around the house you'll see what I mean. You will adapt, but it takes getting used to (and adapting fast is good defense).