I wouldn't say a mirror is necessary, but they are useful. I rode for many years without one, and never really felt the need. I tried a helmet mirror for a few days - didn't like it. It was impossible to adjust satisfactorily, and the one eyed rear view didn't offer much useful information. I've been using a handle bar mirror for a couple of years now, and I much prefer it. I appreciate not having to shoulder check as often, and it's been interesting noting how patient drivers are in waiting for a chance to overtake, something you can't see without a mirror.

They're also good for checking out the exasperated look on the face of the wheelsucker you just dropped.