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It took me some effort to work out Gerashenko's nice simple example http://mathoverflow.net/questions/1565/can-a-singular-deligne-mumford-stack-have-a-smooth-coarse-space/1584#1584 of a DM stack non-equisingular with its coarse moduli space, which means I must improve my understanding of coarse moduli spaces.

What are your favourite examples of coarse moduli spaces? One per answer, please, so we can rank them.