I tend to favor a more side-on stance, as has been mentioned before. In sparring, I keep my hands moving as much as possible, without flailing, anyway. I also don't tend to stay in stance, but prefer to move, keeping as much of my side to my opponent as possible.
On the street, I agree with theletch1: I would subtly slide one foot back and try to get my side presented to my opponent, just in case. Then, I would try and talk my way out of it as best as possible.
When fighting or sparring, I tend to keep my gaze at upper chest/shoulder level. That way, I can get a good overall view of what my opponent is doing, and I don't get fooled by someone trying to trick me by using eye clues.
Seems to work pretty well, most of the time.
Peace--