What do you call a government when the rulers are gods?

Question

I'm familiar with most -ocracies. And I don't mean a Theocracy (rule by religious officials). This would probably make more sense in a Fantasy setting (say D&D) where deities actually come down and mess around with the mortals. However if one (or more) deities took it upon themselves to rule, what would this be called?

Answer 1

Theocracy actually stems from Greek which means "rule by the gods":

The word theocracy originates from the Greek θεοκρατία, meaning "the rule of God". This in turn derives from the Greek words θεός (theos), meaning "god", and κρατεῖν (kratein), meaning "to rule." Thus the meaning of the word in Greek was "rule by god(s)" or human incarnation(s) of god(s).

The EtymOnline entry agrees, saying:

1620s, "sacerdotal government under divine inspiration" (as that of Israel before the rise of kings), from Gk. theokratia "the rule of God" (Josephus), from theos "god" (see Thea) + kratos "a rule, regime, strength" (see -cracy). Meaning "priestly or religious body wielding political and civil power" is recorded from 1825.

So the modern usage--power by "priestly or religious body" is a later usage, but theocracy literally means "rule by gods". If you want another word, however, I would suggest the neologism deiocracy or deocracy, stemming from the word deity.