Somebody in this thread (or was it in the "Is Warlock broken?" thread) that said it would be cool to see a Divine caster that was somewhat analogous to Warlock: i.e., a caster working on a different mechanic and refreshing on short rests.
Now what I'm picturing is a class based on the premise that a God/Goddess "touches" an individual with a kind of madness.
A Cleric has formally studied his deity, and serves as a kind of representative, and identifies himself as such. It's a voluntary relationship. This new class, on the other hand, has some intrinsic qualities and or performed actions that drew the attention of the deity. It wasn't voluntary. He might not really know much about the deity, or claim to represent him/her/it, but he's aware of (and possibly unimpressed or even annoyed by) the relationship.
The crazy hermit is the obvious archetype, but all kinds of fun RP concepts would work.