One of the things I decided early on about my Dwimmermount campaign was that the actual existence or non-existence of the gods would be a matter of debate, even within the setting. The mere existence of clerics offers no help on this score, since clerics are just magic-users by another name. The traditional OD&D spell list is likewise of no assistance, since commune, contact other plane, and even speak with dead are all sufficiently vague in their effects as to raise almost as many questions as they answer. Certainly none make it clear that there are gods, only that there are intelligent entities beyond the mortal realm in which the player characters operate.
Indeed, in the world of Dwimmermount, demons, who are exemplars of Chaos, boast that humanity's hope in the gods -- and humanity's alone, for no other race worships gods -- is utterly misplaced, for there are no gods. Of course, demons have a vested interest in convincing humans to abandon their faith in the gods, so many, if not most, assume them to be lying. Of course, the demons' insistence on this point is troubling, since there really aren't any other examples of "extra-planar" entities to contradict them. I have no angels or devils in my campaign world and elementals care nothing for the affairs of men. Consequently, there's no easy way for anyone to confirm or deny the existence of the gods.
That doesn't prevent there being religions, of course. To date, three religions have played roles in the campaign. The first is that of Tyche, or Lady Luck (or even The Lady), as she is known. Her faith honors boldness of action and the acceptance of the reality that one can do all the "right" things in life and still suffer in spite of -- or even because of -- it all. There are no stories of Tyche ever walking the earth or doing great deeds on behalf of men. It's quite possible that "she" is nothing more than a personification of a philosophy about the nature of fate, free will, and destiny. Turms Termax was once a mortal man, or so the legends say. There are many stories of his former existence, including relics and sites associated with them, but since his apotheosis, he has not seen fit to return to the world in any form. Typhon, the Lawful (Evil) god of rulership, order, and civilization is much like Tyche: devoid of any stories of his actions on earth. His priests are among the foremost defenders of civilization against the depredations of Chaos and it's possible "Typhon" is just a focus for the devotion rather than an actually existent being.
Or not. The point is that I've made a concerted effort to ensure there is some mystery about the nature of the nature and existence of the gods. I think this lends a stronger swords-and-sorcery feel to the setting and it gives me lots more scope to describe a world in which "faith" is religion bears some resemblance to its real world counterpart. Likewise, by muddying the waters about the gods, it makes the nature of alignment much clearer: it's a statement of what and for whom one fights rather than being a shorthand for one's personality traits and moral philosophy. So far this arrangement has served me well and I look forward to seeing where it takes the campaign in the future.