Recently I realized that when I brawl I tend to watch my character rather than my opponent's. And while it may not seem like that would make a big difference because you and your opponent tend to be close together, I think it does. Because you know exactly what you're doing just based on what buttons your pressing (and you can figure out spacing and stuff because you can still tell what your position is in relation to that of your opponent), but it takes longer to read what your opponent's doing out of the corner of your eye.
Recently when thinking about it I've made a point of looking at my opponent's character rather than mine, and I really have found myself doing better. It's easier to place attacks and to avoid those of your opponent, because you can figure out what your opponent is going to do more quickly. But when I'm not actively thinking about it my eyes always stray back to my own character.
Where do you guys look when you play?