"He did not often feel the need for a physical expression of his religious feeling. Like Brion [his deceased brother and the last king], he preferred to witness for his faith through the example of an upright life, rather than spend overmuch time on his knees, in a building that took the place of belief for many folk."
Picture an author at work, creating a hero. The notes and the drafts cover many traits: height and weight, the color of his hair and eyes, what clothes he wears, where he lives, where he went to school, what family he has, even his favorite food and the playlist on his mp3 player. References to all these things and more are worked into the story, but one topic doesn't come up much: his religion. Not that he necessarily doesn't have one (he might or he might not); he just doesn't talk about it, and the world in which he moves, while it has one or more thriving religions, doesn't make a big deal of it either. Why is that?
Obviously, most authors want to appeal to as large an audience as possible, and one way to do that is to reflect the audience and their world in the work. Depicting a lot of church services that aren't plot relevant may bore the audience, taking a particular religious stand may turn some people off, and most people are neither holy rollers nor antagonistic atheists. Conversely, some authors write for a niche market of conversion stories, and starting the target of the conversion in this middle-of-the-road place is both more likely (a devout member of one faith is less likely to change to another) and more common statistically speaking.
The Law of Conservation of Detail can be a factor. If a given plot doesn't require a character to be in a church service, the audience won't see him in one. Over time, this can lead to the audience assuming this character doesn't have a religion or doesn't practice it much. Other aspects of a story may simply preclude religious participation, such as a character working in a demanding job or on an unusual schedule. More obvious examples show these characters interacting with religious figures (usually due to plot demands) so that the topic of religious practice (and his lack thereof) comes to the fore. In these instances, the character will express his religious apathy overtly or have it described or both. Occasionally the issue may be sidestepped by having them attend the Church of Saint Genericus without ever mentioning denomination.
Many other reasons for downplaying religion involve characterization. Perhaps our hero prefers to live his creed rather than profess it much; for this guy, his deeds are his devotions, and "God helps those who help themselves." Then again, perhaps he's compartmentalized his life; he goes to church once a week and the rest of the time he's getting on with the business of living. (These cases have some overlap with the Nay-Theist.) Maybe he's a believer who's uncomfortable with asking for divine help or bothered by the idea that Somebody Up There might be taking an interest in him (If God Is Evil or a jerkass, can you blame him?).
Note that the in-universe society might have a common religion that everyone presumably follows (such as medieval settings or other places with a dominant religion), or it may have many religions with no one sect that's predominant (the USA being a major example). Also note that this hero may not believe in a deity at all and finds it a waste of time to dispute the matter with others. The hero's secular nature may only become clear if/when religious topics are addressed. For whatever reason, this guy has better things to do.
This trope is neither Hollywood Atheist nor the Flat Earth Atheist, who holds back belief despite evidence to the contrary. In works with Physical God(s), a character who acknowledges but does not worship them is a Nay-Theist.
See also Church of Saint Genericus.
Much of the SSS in Angel Beats! initially thinks that they're living some kind of Hell (even though they know they're dead) and swear their vengeance against the god who put them there. As such, most of them aren't too vocal about their religious preferences, especially the SSS's leader, Yuri Nakamura.
Edward Elric from Fullmetal Alchemist claims not to be interested in religion, even though he's met God. However. He didn't know it was God at the time. The Truth isn't visually represented by anything your standard God would look like.
Ciaphas Cain kinda lives in a violently theocratic civilisation where not worshipping the God-Emperor of Mankind is punishable by intense physical torture and, eventually, death (or simple burning at the stake), but Ciaphas is a fairly quiet man on the topic of religion and doesn't engage in much directly religious; he thinks the Emperor is too busy fighting the countless forces of Warp to care about him, personally.
Despite the medieval setting and the presence of many clerical characters, some characters in the Deryni works are less than devout.
Nigel Haldane: The opening quotation describes him preparing to have his nephew King Kelson trigger some of the family's arcane powers in him. Given that he's facing an unfamiliar arcane ritual that also makes him confront the unwelcome possibility that he may become king himself, he feels the need to pray: "A little awkwardly, then, he bowed his head and framed his thoughts in a far more formal petition than was usually his wont..."
Alaric Morgan fits as well, partly in contrast to his more devout cousin Duncan McLain. Morgan once used his magic to contact his aide-de-camp during a religious service, and used fasting as a cover/excuse when he fainted from the effort. The morning after the knightly accolades of Kelson, Conall, and Dhugal, Morgan arrives late to an Ash Wednesday Mass, having stayed up to celebrate with Nigel and an excellent port the night before. He is elsewhere described as being uncomfortable with the idea of receiving the attention of Heaven. He does ask his cousin to give him a blessing (after said cousin became a bishop), and Duncan expresses some surprise at this request; it happens on the day Duncan (who is like a brother to Morgan) was leaving on a military campaign, with the unspoken possibility they night not see each other again.
With the notable exception of Brutha of Small Gods, who is more spiritual than religious despite caring for an avatar of his God, none of the Point of View characters in the Discworld pay much attention to any of the Disc's many gods.
Although Moist von Lipwig does get minorly involved with several during one of his schemes to get the post office up and running.
Harry Dresden is not religious, despite working for archangels, being friends with holy knights on payroll from God Himself, and seeing how incredibly powerful faith can be. He is a direct inversion of the most common application of this trope — instead of being too heroic for silly little churches to bear his awesomeness and insight, he adores religion, but thinks he's not a good enough person to be associated with it.
Father Kienzle, of Robert Koessler's murder mystery series, lives a life largely of quiet faith, laughing at the more ridiculous rituals of the church and bending the rules where he feels it leads to a more harmonious conclusion.
Since Everworld is about kids from our world in a setting full of Physical Gods, the author decided to address some religious issues. April is staunchly Catholic, and Jalil is staunchly atheist; both simply refuse to believe that the super-powered beings they interact with are "gods" in any meaningful sense of the word. David and Christopher seem to fall into this trope, though we know David is ethnically half-Jewish. Senna is more complicated: she grew up when her mom was going through a Wicca phase, and presumably she went to church when she moved in with April's family, but for the most part, she only worships herself (and turns out to be running a cult).
Bill Adama from Battlestar Galactica (Reimagined) does not believe in the Gods. This leads him into conflict with President Roslin on several occasions. Adama's theological views evolve in the course of the series from atheist to non-religious believer.
Jeff, the main character of Community, is agnostic and opts for not talking about religion to keep the peace in the study group, whereas all other characters have relatively strong religious or atheistic beliefs:note Annie is Jewish, Abed is Muslim, Shirley Christian (specifically Baptist), Troy a Jehovah's Witness, Britta atheist, and Pierce belongs to a cult referred to as "Reformed Neo-Buddhism". "To me, religion is like Paul Rudd. I see the appeal and I would never take it away from anyone, but I would also never stand in line for it."
On Buffy the Vampire Slayer,Buffy uses crosses and holy water to fight vampires and demons, but never really ponders the religious implications of that. At one point a new vampire asks about the existence of God and she notes that she knows "nothing definite." (And this was after she'd been to Heaven.) The only legitimately religious characters on the show seem to be Willow and Tara, whose Wicca falls squarely into Religion is Magic territory, and villains (whether they worship demons, Glory or the First Evil).
In Firefly, Shepherd Book is a Christian preacher, and Inara is apparently Buddhist. The other characters don't have a problem with an open display of religion, but Mal most definitely does. "You're welcome on my ship...God ain't." However, a flashback to the Battle of Serenity Valley has him kissing a cross for luck and expressing religious beliefs. It's heavily implied that due to the Browncoats losing the War, Mal has lost most of his faith and become very angryat God as a result.
Dragon Age II - While her late husband was a Church Militant, Aveline is the closet thing the game has to an agnostic and states that she married a man but not his religion. Sebastian, Carver, Bethany, and Anders are all Andrastians (though the latter two have issues with The Church), Fenris goes back and forth on how much stock he puts in religion, and Merill worships the old elf pantheon. Isabela comes one of the few non-Andrastian human nations and Varric is a surface dwarf who treats his race's ancestor worship with some irreverence.
Aveline: I have heard the Chant. It is lovely; perhaps that's all it needs to be.
Also from Bioware, Commander Shepard of Mass Effect will only have his/her religion established in one conversation with Ashley; your options range from expressing shared belief to respecting her right to her religion to straightforward mockery.
Sonozaki Shion of Higurashi no Naku Koro ni is a great example of this trope. She's sent to a Catholic school (against her will) and escapes, later on saying "If I stayed in a place like that, I'd either end up brainwashed or insane!" She also denies the existence of the village god, Oyashiro-sama on a lighter note.
Bureaucratic Deva: Let me ask you something. Why did you never consider becoming a cleric yourself? You have halfway decent Wisdom and Charisma scores, you could have pulled it off. Roy: Well, this is awkward to say, given where I am, but I've never really been that religious. I mean, I guess my mom raised me to worship the NorthernGods, but I always just figured as long as I don't actively offend any of them, they'd leave me alone.
One episode of Family Guy has Lois learn that her mother was originally Jewish. She experiments with the religion a bit, but ultimately concludes that she doesn't really care about either it or Christianity, despite the family being church-going in other episodes. (Of course, this was a later episode, so whether we can call any of the Griffins "heroes" is arguable.)