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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.

Would an administrator please tag this question "coarse-moduli-spaces", please?

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What are some examples of coarse moduli spaces?

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.

Would an administrator please tag this question "coarse-moduli-spaces", please?