I've never been in a situation where I felt a mirror saved me. But I've been riding with one for the last 5 years and feel unsafe without it.

The tangible benefits I've had are:
1. Finding a space to move over in traffic
2. Knowing that cars are coming up behind me from a greater distance than my hearing. I usually only use this if I'm riding in the lane I'll move onto the shoulder if it's safe to do so.