A long-standing beef many gamers have long had with D&D's magic system as written is that it functions identically for both clerics and magic-users, even though clerics are generally held to receive their spells from their deities rather than through memorization. I say "generally held," because OD&D never made this connection explicit, although, to be fair, AD&D did and that edition has exerted the strongest influence over the game's development over the years, while OD&D is relegated to being an evolutionary "dead end."
That's unfortunate, because the AD&D's interpretation makes no sense. If clerics and magic-users both use the same game mechanics -- memorization, spell slots, etc. -- then why do they use two entirely different spell lists? Likewise, why do they learn spells at different rates? Simply saying, "Because the gods grant a cleric's spells" isn't a solution, since it only highlights that, if a cleric's spells have a different origin than a magic-user's, then they should use different mechanics -- at least that's what it says to me.
You'll note, though, that I say "if a cleric's spells have a different origin." That's because I've come to believe that they don't have a different origin and the only way to make sense of the similar but not identical mechanics for both spell casting classes when it comes to magic is to assume that all magic has the same origin. OD&D never spells out this origin and that's for the better, since it lets each referee decide for himself what best suits his campaign. Nevertheless, reading between the lines, it's easy to get the impression that magic is some kind of "natural" aspect of reality that spell casters know how to tap into and manipulate to create various kinds of effects.
If that's so, what differentiates a cleric from a magic-user and why do they have very different spell lists? Again, OD&D isn't explicit on this point, but it is suggestive. A cleric has Wisdom for his Prime Requisite, while a magic-user has Intelligence. Under OD&D as written, neither of those ability scores has any game mechanical effects, except the determination of the experience point bonus (if any) the character receives. And yet the rules specify two different abilities as the Prime Requisite for these classes. What does that suggest? To me, it suggests that Intelligence and Wisdom represent two different "philosophies" or approaches to magic, the former about understanding the ambient energies of the universe in order to control them and the latter about using those energies to achieve enlightenment -- in short the Way of Intelligence and the Way of Wisdom.
Under my interpretation, both are "sorcerers" in a broad sense, for both tap into the same universal power source. The difference is that magic-users bend that power to their wills, which is why they acquire spells faster and their magicks are generally destructive and self-aggrandizing. Clerics, on the other hand, bend themselves to match the warp and weft of the universe's power; they improve themselves in accordance with its laws. Many clerics use gods -- who are more truly distant "supernatural" beings -- as foci in this process of magical enlightenment, but not all clerics do so. Many are reclusive hermits or wise men who achieve wisdom without the need for intermediaries. OD&D clearly supports this, since the rules barely ever mention gods at all or their connection to clerics. Likewise, both pulp fantasy and chivalric romances, both of which were major influences on OD&D, often include the character of a wise old man with the ability to heal or read the fates without any explicit notion that their powers are "divine," even though both abilities are closely tied to the D&D cleric archetype.
But what of evil clerics, which OD&D calls, suggestively, "anti-clerics?" My own feeling is that such individuals are twisted reflections of true clerics. Under the direction of their foul deities or, worse yet, demons and devils, they seek to put the Way of Wisdom toward corrupt ends. Like shadows, though, they cannot exist without the light. Evil clerical magic is thus a mirror image of the good, a pale imitation. Under OD&D rules, anti-clerics could only cast the reversed versions of clerical spells and I think this notion works well with my interpretation.
Like many aspects of D&D, its magic system isn't one that can withstand close scrutiny, as it's mostly a convenient game mechanic rather than a carefully considered metaphysical system. Nevertheless, I think the system we have can be made to work in a way that's more internally consistent, flavorful, and evocative of the game's pulp fantasy heritage.