I never ran or played in a Greyhawk campaign, but I did get the 1983 boxed set as a kid. Reading it today for the first time in many years, this passage caught my attention:
The people of Oerth worship many gods. Only deities of the central Flanaess are detailed here, and of those, only the lesser gods (in most cases) have been detailed. In general, the greater gods are too far removed from the world to have much to do with humanity, and while they are worshiped, few people hold them as patrons.
These deities have been known to intercede directly in the affairs of men... a demi-god and a godling might well become embroiled in human affairs...
In my games, the gods—big or small—remain distant, their existence implied only by the granting of cleric spells, which is strange, since my imaginings about such things were founded on youthful readings about Homer's compulsively meddling, all too relatable pantheon. Maybe that one DM who used an uber-powerful archmage to lead our characters by their noses through his epic Lord of the Rings knock-off made me over-vigilant.
I'm changing-up to radically familiar gods in my new campaign. These minor deities have only a handful of spell-casting clerics, and they appear personally to replenish spells.
Imagine: you're a cleric, sleeping after an exciting adventure that exhausted you and all your spells. At some point in the night, your god—with his sweaty hands (or pseudopods or whatever) and coffee breath—shakes you awake and whispers divine revelations in your ear. Sort of like Santa Claus or your creepy uncle.