It could be an imbalance in strength between the two sides of your body. For example, if your right leg is stronger, you may lean ever so slightly to the right, and it takes a 7' barbell for anyone to notice. Or for the same reason you could be unconsciously setting yourself just slightly off center on the bar (I have a friend that just recently noticed that he does this). A flexibility imbalance in your arms/shoulders could place you off center too.
I actually really dislike mirrors myself, because the distraction is way too much cost for the benefit during the lift, though that's just personal preference. Could help to make sure that you're centered on the bar though.