I stopped using mirrors, with the single exception for shaving, years ago. My car at the time had no rear-view, and some kid crashed his bike into the driver's side mirror (which flew off a good 10 meters). Since then I've become used to turning the head to check. This actually has one notable benefit for riding a bike -- it lets other vehicles know that I am aware of their presence. I can make eye contact and show body language which helps greatly to show my intentions on the road.

Riding a bike (in a straight line while avoiding obstacles) while looking backwards is a skill that I am very glad to possess.