In my campaign, I still use an idea from 1E: Strength of faith alone can grant access to low level spells. Demigods can grant lesser powers, and lesser and greater gods can grant even greater powers directly.
I altered it, such that clerics with NO deity at all can get up to 3rd level spells; so, anyone who strongly believes in a god of bottle washing can get up to 3rd level spells.
Demigods, and divine agents of that level of power, such as high demon and devil lords, can grant up to 6th level spells.
Lesser and Greater Gods can grant up to 9th level spells, but must do so directly.
There is even a city in one part of my campaign which is BASED on religion. It started in concept as a place similar to the Greek Parthenon, where temples of all gods were gathered in one place; but, as different religions paid heed, more and more gathered. The city now OVERFLOWS with temples and shrines to different gods, and only 20 or so can actually claim to be temples of known gods; the rest place their faith in gods that few have ever heard of, and desparately trying to win converts in order to increase not just their standing, but to actually gain enough power to MAKE the god manifest.
In my home campaign from whence this comes, there is a sharp divide between Arcane and Divine Power. Until a certain event in the campaign's past, the ONLY way to get any magical power was through following a god. After this historic event, Arcane magics could be tapped and harnessed. One of the world's central themes is the conflict between followers of gods, and those who say mortals NEED no god. Originally, the divide was pretty clean - there was no healing available without intercession from the gods, and there were no clerics casting fireball, or meteor swarm, power words, etc.
THEN, the bards stirred things up.
Before, Bards could not manifest healing magics. Now, within the last few years, Bards have arisen able to tap healing magics, WITHOUT venerating or at least calling on the name of a god. It has thrown the priesthoods into an uproar at the highest levels, and they fear a bard or a wizard may yet arise who can raise the dead. The priests of the God of Death are REALLY looking for such an individual, and if they find one who can demonstrably raise the dead... *skkkkkkkkkkkkt* (sound of finger-across throat)
However, a curious thing also happened, that the Arcane workers have largely ignored, but the implications of which have struck those in the know: Clerics are starting to manifest higher level Arcane Magics. However, whether this is the gods who are "fighting back," or some unknown confluence of Arcane and Divine beginning to be unified, none have ANY clue.