One of the many interesting ways that Dungeons & Dragons differs from its literary forebears is in the matter of religion. Pulp fantasy, by and large, is unconcerned with the subject. Priests are generally portrayed as hypocrites at best and outright villains at worst. Likewise, the actions of the gods, if they occur at all, are mysterious and easily written off by the skeptical as mere chance. This clearly isn't the case in D&D, where, thanks to the inclusion of the cleric, religion has always played a role in the game.
Granted, the cleric owes the better part of its existence to Hammer horror films, but, if you read OD&D, you can see that the class quickly evolved beyond its origins as a mere vampire hunter-cum-medic. The influence of historical medieval wargaming on the game shouldn't be overlooked. Everyone remembers Chainmail because of its Fantasy Supplement, but Jeff Perren and Gary Gygax didn't write these rules in order to facilitate miniatures battles between dragons and elves but instead to recreate the warfare and technology of the European Middle Ages. Gygax, by his own account, was very keen on medieval history, at least on the military side of things (no doubt the source of his pole arm-philia). Given this, is it any wonder that the armored, mace-wielding cleric bears a strong resemblance to the religious knights of the Crusades?
If you read OD&D carefully, you soon notice that a lot of the paraphernalia associated with clerics has Christian origins. The equipment list, for example, includes wooden and silver crosses, not the "holy symbols" of AD&D and later editions (Interestingly, there are no crucifixes, which I think is significant). The cleric's level titles include a number of specifically Christian terms (vicar, curate, and bishop). The illustrations of clerics in OD&D -- and even early AD&D -- always show them dressed in obviously Christian priestly garb. And of course many of the cleric's spells draw on Christian (and Jewish) religious writings and folklore. Indeed, the cleric's focus on defense and protection spells is, I think, more evidence of the Christian origins of the class. What's even more telling is the fact, even as late as Eldritch Wizardry, there are few (if any) explicit references to gods in OD&D. There's much talk of demons, devils,and, tellingly, saints, but gods aren't much talked about until Supplement IV's release in 1976.
I once asked Gary Gygax directly about the question of why this was so and he explained that he felt it unseemly to include anything too explicitly Christian in a mere game, even if he assumed a kind of quasi-Christian or crypto-Christian underpinning for the whole thing. This is also why his demons and devils used somewhat obscure names rather than very familiar ones. All the old school love for statting up Satan/Lucifer was something Gary didn't feel was proper. It's the same reason why, even in late AD&D, we get planetars, solars, and devas but never "angels." Interestingly, the original Blackmoor campaign, as I understand it, had a Church, complete with a hierarchy, but no named gods. Again -- and someone can correct me if I'm mistaken on this -- there's an assumption of a quasi-Christianity lurking in the background.
Reading Chivalry & Sorcery as I have been, there's a bit more explicit assumption of Christianity there, but it's still stated in a somewhat circuitous fashion -- an oddity given the great detail given to things like ecclesiastical structures, beliefs, relics, and so on, not to mention the lengthy bestiaries of demons (including Lucifer himself). In the case of C&S, the impression I get is that its authors simply assumed that their readers wanted their games to include lots of quasi-Christianity, since it was more "realistic" than the henotheism of most fantasy RPGs. I know that, in my early days of gaming, my friends and I all tacitly assumed that clerics were Christian priests -- heck, I thought monks were as well -- and that, somewhere, behind all the monsters and magic, the Lord of Hosts was lurking.
We never really talked about this assumption or dealt with it in any direct way, but we neither did we question it. It was an odd kind of Christ-less Christianity, more concerned with laying the smackdown on evil than with turning the other cheek or taking up one's cross, except in the most vague of senses. The paladin was an unambiguously Christian knight for us and indeed Lawful Goodness we associated with this unspoken religion that had bishops and cathedrals and holy water and everything else a young boy saw as being "essential" to medieval Christendom.
As time went on and our sense of D&D changed, this implicit Christianity became less important, but it never fully faded away, because it just seemed to us that there was just no other way to look at the cleric and the paladin except in the context of quasi-Christianity. Nowadays, I'm probably too immersed in swords-and-sorcery to fall into this perspective again, but I am now more firmly convinced than ever that early gaming, far from being "pagan," was in fact shot through with Christian belief, practice, and lore. It was always a kind of "fairytale Christianity" broadly consonant with American generic Protestantism rather than anything more muscular, but it was there and it's never really died, even if all the post-1e editions of D&D have tried to varying degrees to remove all evidence of it. I find it fascinating to remember this, if only because, as I spin off in flights of pulp fantasy fancy, it's good to be reminded that D&D owes its origins to more than just that style of fantasy and is in fact a goulash of unspoken and contradictory inspirations.