In a D&D context, it's hard to imagine gods intervening without nuking the PC's out of existence. A god gets pi$$ed, and he wipes out most of the human race with a worldwide flood, or immolates a couple of cities, or causes an evil kingdom to lose an existential war.
In most D&D universes, characters of the Cleric class get their power directly from the god they worship. Sometimes, bonus spells are granted to the uber faithful.
This may be true of the Hyborian Age, but, then again, it may not. Is Sorcery a science with absolute and direct cause and effect? Or, is it a gift (or a curse) of a demon...or a god? We don't quite know. I like the mysterious aspect of sorcery (and mostly, of the gods, sans a few instances) during the Hyborian Age as opposed to typical D&D worlds.