Cyan's observation about mixtures of conjugate priors being conjugate kills the example I had in mind. Ill think for a bit and let you know if I think of any examples. If I haven't replied in a couple weeks, remind me and ill make sure to reply.

Dirichlet processes aren't inherently hierarchical, they are just self-conjugate, so you can make the output of one the input to the other. If you connect them up in a tree structure, you get a hierarchical dirichlet process.