I have to say, I am quite surprised at the replies in this thread.
Regardless of if you are training for strength or bodybuilding, mirrors should play a huge role.
For strength training, unless you have a coach and someone watching you all the time, a mirror is invaluable for assessing your technique. Sure, once you have perfect technique, you may not need it anymore, but every so often it would still be good to make sure you are still hitting depth on squats, or looking up, or whatever you want to be doing. Even with something simple like bicep curls or whatever, you might find you are cheating more than you thought you were, or that your elbows were flaring out or whatever. Without a mirror or a coach, how would you know?
For bodybuilding, there is no question. Mirrors are invaluable. It is not about looking in the mirror and admiring yourself, it is about looking in the mirror and critiquing, looking for ways to improve. How else can you tell if you are getting closer to your goals?
More importantly, mirrors are great for motivation. When I look in the mirror and no longer see a scrawny little kid, it makes it a lot easier to get motivated to push out that heavy set, or to get out the extra reps.
It helps to assess bodyfat changes, changes in vascularity etc etc. All things that an aspiring bodybuilder should be keeping tabs on, or just anyone interested in their appearance.
I find it hard to believe that anyone training doesn't care at least a little about their appearance. Even many people on this site who claim not to care and don't use mirrors etc, but still post up pics every so often... And if you care even the slightest about your appearance, then improvements in your appearance should be highly motivating.
On a related note, what is so bad about flexing in the gym? I don't do it often, but after a really good set, I might pull a most muscular or sometihng, see if the vascularity has changed. It is purely for my benefit and nobody elses (I usually go into a corner, or the changerooms first lol)