A lot of mirror-haters will tell you that a mirror is no substitute for looking back, and that you don't need mirrors because the purpose they serve in cars does not apply to bicycles.
It's true that cars use mirrors primarily for backing and checking the blind spot before changing lanes. These things don't apply to bicycles. We normally don't back up and our peripheral vision is good enough to see our so-called blind spot.
But there is other vital information that a cyclist needs from a mirror that cars do not need. When I'm in my car, driving down a two lane road at 60 mph, I don't really care if there is a car 200 or 300 yards behind me. If there is, I'm also not too worried about how fast it's going. In my car, I'm going fast enough that even if the car overtaking me was going 90 or 100 mph, the driver would most likely see me before he rear ended me. In other words, I don't need to worry about getting out of his way any time soon.
Now, if I'm on the same two lane road riding my bicycle, I do worry about cars 200 or 300 yards behind me and how fast they are going. That is where my mirror comes in very handy. If I see a car behind me, I can keep an eye on it with my mirror and ascertain how fast it is going and how soon it will get to me. Moreover, as it approaches me, I can determine if the driver has seen me by whether or not he starts to move over to pass me or slows down due to oncoming traffic that prevents him from passing me.
A few times, I've seen a car in my helmet mirror and watched as the driver did not slow down or move over. With that information, I determined that I needed to get myself onto the unpaved shoulder because there was a good chance that the driver did not see me. In those situations my mirror probably saved my life because just "looking back" would have told me the car was there, but not given me any information about it's speed or driver's attentiveness.