Much as in a car, mirrors can be very useful in increasing your traffic awareness. They are particularly useful when cycling in a built up area (or come to that on a dual carriageway so that you have some warning before the juggernaut comes thundering past).
Many are put off by traditional mirrors, which can be quite bulky, but there are a number of small, sleek versions now available for a range of bicycles. You can even get stealth aerodynamic ones for racing bikes which plug into your drop handlebar ends.
For years now I have been using Sprintech Road Drop Bar Mirrors. They weigh nothing (well, not nothing but as good as) and are almost unnoticeable. They are quite expensive but they come as a pair and you only really need one on the right, so you can kit out two bikes (if you are lucky enough to own two) for the cost of one.
I have also found that, as I get steadily older (no matter what I do I just can’t seem to avoid it) my dexterity is diminishing and casually glancing over my shoulder is becoming more and more of an effort. Being able to see behind me by merely glancing down is a great benefit. In fact I now do it instinctively every few seconds, again like checking your mirrors in a car. I realise this every time I ride a bike without mirrors and find myself glancing down at the tarmac all the time, where the mirror should be.