Reading a post in a blog far more popular than mine, my imagination wandered far off from the writer's points. He says we're all doing it wrong with polytheism in D&D, but... I don't know, I've never really cared about recreating Roman polytheism in detail, because among the many things I am not, I am assuredly not a religion major. What I do want to talk about is a bunch of different neat ways I've seen religion done in fantasy and fantasy games, in no particular order.
The Gods are NOT Your Friends - Shattered Isles, HP Lovecraft
Shattered Isles - Drakhara
Cultists are rare (aside from Drahathi)
No proselytizing, but open to making deals
Active in the world; often physically present
Can be killed
Responsible for creation
Few-if-any cosmic-level servants, temples, or other "holy" sites
SI's Drakhara were Elder Gods, involved in if not responsible for the creation of the world, and they were inimical to mortals, though not universally malicious. (This is all based off of what I recall from the campaign, and thus is subject to dispute from others who were better informed on this particular topic.) From the mortal perspective, these beings were enemies and should be destroyed at absolutely any cost, including the potential ruin of a whole nation. Banishment to the Outer Dark was also possible and used in one case, though it required a complex set of circumstances (and a really good gimmick battle).
That's the main difference, then, between SI's Drakhara and Lovecraft's famous Mythos. The Drakhara were in the world and active Right Now, and it was possible to destroy or banish them - a far more humanist approach, since the game was intended for long-term play and player involvement. SI needed further to allow conversational interaction with its villains to get across much of their characterization. To this end, one Drakhara was killed in the climax of the first campaign, through an interesting set of circumstances, and one was teleported away to the Outer Dark about midway through the second campaign. N'goloth had individual mortal or formerly-mortal servants (not really characterized as cultists), while the Gathi had the Drahathi elves in his service (those who had once been oathsworn to keep him bound - and thus known as the Oathbreaker elves) - still not exactly cultists, though I never did learn why the Drahathi did what they did; they were, in any case, significant recurring opponents over nine years of play. Drakhara didn't proselytize, though they did cut deals - and once they had their hooks in you, they absolutely never let go.
Cultists are common
Cults recruit; the Elder Gods drive mortals mad, causing them to become worshipers
The gods are asleep or outside of reality
Cannot be killed
Destructive to all of reality; involvement in Creation is unclear
Some sites resemble temples; some have heralds or other cosmic-level servants
Lovecraft's various Elder Gods cannot possibly be killed by the meager forces arrayed against them. In the generally-accepted "correct" approach to Lovecraftian gaming, the PCs are absolutely never going to kill Cthulhu, Nyarlathotep, or any of the others, but those gods either sleep or seek to intrude from outside of reality, so the PCs have the potential (and nominally achievable) goal of keeping them in slumber or preventing their entry into the world. These beings are so utterly alien that conversational interaction with PCs would be pointless, would strip away what makes them the unknowable horrors that they are. As far as I know, most Elder Gods have human or near-human cultists, just to give PCs something to fight in the early part of their very brief lifespans. (I mean, all of those guns that PCs have learned to use might as well be valid weapons against something.) The closest the Elder Gods come to proselytizing is driving people mad enough with knowledge of their existence that they come to serve - it's not entirely clear to me why cultists decide to sign up in Lovecraftian horror.
The Gods are Primal Urges - Shattered Isles (elements), King's Gate (Altera, Totems)
Shattered Isles - Elements
Either you're born with a tie to an element, or you have no particular reason to interact with the Elements. The elements are not really in competition with each other.
The elementals have certain expectations of your behavior
Elementals are active servants - both as enemies and allies
The Elements cannot, in concept, be destroyed, but could be manipulated or corrupted
These are the building blocks of creation
PCs can become cosmic-level servants as a retirement option
Dorums are... sort of like elemental temples
From a certain point of view, SI's six elements and sorcery were the PC-friendly gods of the setting, with elementals as something like divine messengers. Tal Elan and Tal Shar had the ghosts of those who had gone before as their comparable but quite a lot rarer messengers. Dark Sun presents gods in a similar elemental form. Some campaign settings that follow this pattern give them personal names, and some have clerics of Fire, Water, and so forth. In each of these cases, there's really no purpose to proselytizing - insofar as someone worships or serves Fire, it's typically acknowledged that other choices within this paradigm are about equally valid. These gods tend to be pretty disinterested in humanity overall, but will grant them favors if importuned in the right manner. SI's elementals, for example, would teach spells and undertake various tasks more-or-less willingly if fed a fistful of Essential Elements - accreted, solidified energy harvested from ley lines. In SI, you really only interacted with elementals if you had a tie to that element; a nonmagical person didn't stand to gain anything from the elementals, and neither the element nor the elementals had any interest in their worship or service otherwise.
King's Gate - Totems
You're born with a tie to a totem, or you have no particular reason to interact with them
The totems had very strong expectations of certain behavior; violating these codes of behavior harmed the PC and that person's bonded Ylanni spirit
The totems worked through visions, but otherwise were not directly active in the world; the Ume were active, cosmic-level servants
The totemic powers themselves - Wolf, etc., - could only be threatened by cosmic forces; the "deity" here is actually a collective of all spirits of that type
Not responsible for Creation; the Ylanni wander from world to world
PCs can become cosmic-level servants as a retirement option
King's Gate's first campaign had really no gods, while the second campaign revealed a great deal more about history and cosmology that changed this. The Ylanni, totem spirits to which some people were bonded, were... sort of like animal gods, but again had no interest in any kind of interaction with those who weren't tied to them by a totem bond. In the second campaign, we learned more about the Ylanni, including the First among them to come to the world of King's Gate, who were called Ume. Still, not gods; they were countless and diverse individual spirits, for all that one might refer to the group en masse.
King's Gate - Altera
Worshipers were common in the past; in the present day, only one race is even aware of them and still worships them
Presumably in the past they had expectations of behavior; in the present day their rites were known only to the kezhekai
Possibly active in the world; few clear expressions of power
Can't be killed because there's nothing to kill or threaten; could be forgotten entirely, though
Might be believed to be responsible for creation
No significant proselytizing
No known cosmic-level servants
Altars in the wilderness or among ruins
The second campaign further introduced Altera, powerful entities that were worshiped in ages long past, but were forgotten in the lore of the modern world. This was an excellent example of creating doubt as to whether these Altera existed as real, conscious entities at all, or whether they were names applied to elemental dualities and impulses. It seems that there had to have been something behind them, but it is difficult to say what; some incidents clearly seemed to indicate purpose and will. If these beings existed, though, they did have an apparent desire for worship and service. One of the four Altera was not like the other three: where Mena, Talo, and Ia were driven by impulses more-or-less according to the elemental natures, only Runa (as the representative of Tal Elan and Tal Shar) had positive and negative moral impulses. KG did an excellent job of keeping all four mysterious and entirely unknowable.
The Gods are Silent and Possibly Nonexistent - Eberron
Religions vary from cults to philosophies to full-fledged organized religion
All religions proselytize; some are race-locked (such as the Path of Light and the kalashtar)
Gods are completely inactive in the world, and may not exist at all. Clerical power is not tied to divine will or judgment.
Gods cannot be killed or met in person - note that some of them are philosophies anyway
Dragons, not gods, are more often considered responsible for creation (cf. Khyber/Eberron/Siberys)
Cosmic-level servants... I guess? There are certainly plenty of outsiders, anyway
Wide range of temples and holy sites
Coming from a background of predominantly playing Forgotten Realms (see below), Eberron was quite a change for me. The gods of Eberron are distant and mysterious to the point of potential nonexistence, and even characters worshiping things that I am pretty sure are definitely not gods (Blood of Vol) can derive divine magic. Correspondingly, corrupt clergy have just as much spellcasting capacity as true-hearted servants. Faith or rejection of faith are equally valid character decisions. I do not believe I had seen a presentation quite like this in any setting before it, as designers felt compelled to explain divine magic somehow, and never quite came to the "pure strength of belief" answer. (Admittedly, I don't know Greyhawk's canonical stance here.) The desire of the gods to proselytize, then, is strictly a function of whether their existing mortal servants decide to proselytize.
The Gods are Incredibly Powerful and Frequently Present - Forgotten Realms (3.x and before)
Religions vary from cults to full-scale organized religions
All proselytize and compete for dominance; gods need worshipers in order to survive; these religions are generally regarded as race-locked (Moradin for dwarves; Torm for humans)
Gods are pervasive and highly active in the world; most plots are ultimately traced back to a god
Gods can be killed; turnover is common
A single Over-God is responsible for creating the world
There are a dizzying array of cosmic-level servants
Apotheosis or promotion to cosmic-level service is possible and reasonably common
Wide range of temples and holy sites
All gods have expectations of behavior
Forgotten Realms is a setting perhaps best known for its super-powerful NPCs, including (in editions prior to 4th) a pantheon of 120 deities.These deities frequently intervened in the world, particularly in the novels; these 120 were the most important manipulating forces in the world, and truly powerful mortal NPCs could come close to interacting with demigods on equal footing. FR's approach to deities is probably a big turn-off for a lot of people, but I will say in its favor that it makes plotlines unbelievably easy to write - you have a list of 120 characters who want things and have the means to motivate others into action. In a sense, the pantheon of FR has a lot in common with looking at the JLA from the perspective of a totally normal person in the DC universe. FR, as a result, plays into all of my worst habits of putting a wizard or cleric at the helm of every single major happening in my games.
What Is a God, Exactly? - Steven Brust's Dragaera, Arcana Evolved
Dragaerans respect the gods as "people with skills and power"; Easterners worship the gods
Gods have no evident interest in proselytizing
Gods are active in the world; many plots ultimately trace back to Verra's machinations or the Jenoine threatening the gods
Gods can be killed, and in fact a lot of plot energy revolves around this point
The Jenoine, not the gods, made many of the races of the world into what they are. No clue as to who created the world
Demons and undead are sort of cosmic-level servants for the gods. Being a demon or an undead creature has nothing to do with being a bad guy.
Apotheosis is possible; all of the gods were something else first, and many of them were Dragaeran wizards
The definition of the term "god" is a matter of some debate in the setting, though it currently seems settled
There are some temples and holy sites, more common in the East than in the Empire
Dragaera is a really interesting case. In a lot of ways, it feels like Brust set out to write the most incomprehensibly high-powered setting that could be dreamed up, just to prove that he could make it awesome. At this point, the protagonists wield five of the seventeen Great Weapons, regularly converse with Verra, have access to a floating castle with a tower that can teleport them absolutely anywhere... and they still have problems that they find it challenging to solve, simply because they can't or won't just do whatever they feel like doing. The main characters have been called upon to fight alongside a god before, and it was an interesting scene in which they all seemed suitably threatened. Aside from Spellbreaker and.... REDACTED for more spoilage, Vlad is more limited at this point in the series than he was in the first book. Sort of. Anyway, Brust's experiment is an unqualified success in my view, and I can only wonder why I haven't seen one or more Dragaera RPGs.
Religious beliefs vary by race; some races have no religion. No observed proselytizing
Gods vary widely in activity - none grant spells or miracles, but some still act individually
Gods can die; apotheosis is possible
The gods that we know of are probably not responsible for creation
There are cosmic-level non-deific entities, but they are probably not directly affiliated with the gods
Temples are numerous. There aren't a lot of holy sites; places of power (witching sites, etc.) have little if anything to do with the gods
Religions may have expectations of behavior
If you were going to pick a version of D&D 3.x to use to model Dragaera, Arcana Evolved would be a pretty solid choice, once you did a little rules hacking. Some gods have a rock-solid and unquestionable reality in the setting (at least, the setting presented by our GM), since we've received object loresight responses identifying the race of an item's creator as "a god." At the same time, we've never met one in person so far as we know, and there's no clerical magic as such. (I don't think the Mage-Priest prestige class is so much about invoking gods as it is about knowing and uttering names of power.) Much as cultures exist side-by-side without ever really mixing in the setting, so religious beliefs have not crossed racial lines, and each race thinks the other races are weird for believing whatever it is they believe.
It's entirely possible that the setting has no gods other than the ones we've confirmed with magical divination, as described above. The setting books don't give GMs or players much guidance here. Much like Eberron, where the setting book describes a bunch of setting mysteries without resolving them, I regard this ambiguity as one of the setting's major strengths, and I remain curious to see what our GM will uphold or reject for this campaign.
I was going to comment on L5R/Rokugan, but I realized that I just don't know enough about it to speak with confidence. As the Eclipse campaign is still unfolding, I did not attempt to discuss it here; much remains unclear to me about the objective reality of the gods in that setting, and recent conversations with NPCs who are In The Know have caused me to drastically revise some previous beliefs.
It's been particularly interesting to watch LARP settings change over time in the South. Religion in LARPs was once sternly verboten by popular consent, in the sense that we were afraid a "D&D is Satanism!"-style public backlash. SI eroded this rule, in the ways described above as well as the sorcerous orders that had a lot in common with monastic orders. KG's Order of Knowledge took still bolder steps, filling the role of the Church; the Sword of Knowledge was a particularly faithful parallel of the Templars. The Seekers and the Shield included Jesuits, Franciscans, Benedictines, and Hospitalers in their archetypes. To the consternation of the Plot Committee, everyone started the campaign thinking that the Seekers and the Sword were intended as parallels of the Holy Office of the Inquisition.
Eclipse and Dust to Dust, on the other hand, have felt pretty free to include a wide variety of religions. Early writing of Dust to Dust included considerable stress over how some groups, such as the Redwood Throne, might be interpreted, and we went to some lengths to make them less outright offensive while still accomplishing our goals within the setting.
ETA: Seaofstarsrpg brings further scholarship to this conversation with this post.