Where is my faith? Even deep down ... there is nothing but emptiness and darkness ... If there be God—please forgive me. When I try to raise my thoughts to Heaven, there is such convicting emptiness that those very thoughts return like sharp knives and hurt my very soul ... How painful is this unknown pain—I have no Faith. Repulsed, empty, no faith, no love, no zeal, ... What do I labor for? If there be no God, there can be no soul. If there be no soul then, Jesus, You also are not true.
In the Forgotten Realms comics, the elven cleric Vartan refuses to worship his god Labelas—even to access desperately-needed healing powers—after an arc in which Labelas possesses Vartan's body and torments his friends. Labelas shows up later and tries to make amends; Vartan accepts the gesture, and a later short story shows him returning to Labelas' service.
In Signs, Mel Gibson's character is a former Anglican priest who lost his faith when his wife died. The Twist Ending makes him reconsider.
The protagonist of the Diablo Cody dramedy Paradise is a devout Christian who goes through a crisis of faith when she's involved in a plane crash and gets horrific burns on most of her body (but conveniently not the face)
Arthur C. Clarke's short story "The Star" is about a Jesuit priest who has a crisis of faith when he learns that the nova that destroyed a planet of morally good inhabitants was the star over Bethlehem.
The short story isn't a full example, as it doesn't end with the priest getting his faith back. This was "fixed" for the television adaptation.
In Warrior Cats, the whole of ShadowClan stops believing in StarClan after a loner named Sol predicted a solar eclipse and StarClan weren't able to. ShadowClan's leader Blackstar had already been having some doubts because life had been harder since the Great Journey, so it didn't take much for Sol to convince him that StarClan was powerless. They did start believing again, though, after some StarClan cats - ShadowClan's last leader and medicine cat - spoke to Blackstar and his medicine cat.
In The Final Trumpet, an adventure for the In Nomine RPG, the Archangel of Faith himself actually reaches this point, risking Armageddon in the process. Depending on the actions of the player characters, he may come back stronger than ever, or Fall completely to become the Demon Prince of Fanaticism.
Drives a lot of the plot in Dirge for Prester John. John tries hard to be a good Christian king of a kingdom of, in his view, heathen monsters. In the frame story, Hiob's faith is also shaken by John's account of Pentexore.
In Courtship Rite, on the Lost Colony of Geta, repeated cycles of famine have, after many centuries, made cannibalism an accepted part of the culture. The "Gentle Heretic" Oelita, in addition to believing that cannibalism should be avoided, is convinced that humans are native to Geta, despite their obvious biological and genetic differences. When conclusive evidence appears that this is not the case, she begins to question her whole belief system.
I believed in a beautiful god. But this is the true face of the divine.
Due to events at the climax of the second Mistborn book, Sazed (who collects dead religions and considers himself a believer of every single one) spends much of his time in the third meticulously examining each one, looking for a faith that can provide an answer to his questions.
This happens to Omman Knight Jon Ommandeer in Serial 5 in Spectral Shadows, or at least is supposed to according to the serial synopsis. How his faith is in crisis and the extent of it is as of now unknown.
A recurring theme throughout Safehold, as the entire cast save Merlin were raised and taught to believe in a church that is, in fact, a Path of Inspiration perpetrated through a God Guise. While dedicated to the eventual revelation of this gigantic lie many characters, especially Archbishop Maikel Staynair, fear the large scale Crisis of Faith that many will suffer since it's hardly a leap to decide God is a lie after learning your entire Church is.
Even without this knowledge, Father Paityr Wylsynn experienced a Crisis of Faith in the wake of everything that has happened across the first four books. In the fifth book, How Firm a Foundation, Staynair recommends him to the monastery that helped him with similar troubles in his youth and eventually votes to induct him into the Inner Circle of those in the know.
Knowledge Of Angels: Beneditx has one after talking with Palinor, and becoming convinced by Palinor's atheist retorts.
In the Scrubs episode "My Own Personal Jesus", Turk loses his faith in a just God after a hopeless Christmas Eve in the emergency room, but regains it after he finds a missing pregnant woman by intuition and helps her give birth. (Interestingly, Turk is the only character in the episode who professes strong religious beliefs in the first place, and the other major characters seem to look down on him for this.)
In the Quantum Leap episode "Leap of Faith", Sam leaps into a priest, and Al is uncomfortable with the whole thing. He reveals that he left the church as a child, after prayer failed to save his father from dying of cancer, and swore never to have anything to do with God again. However, he resorts to praying to God again when it looks like Sam's life is in danger.
An episode of Dead Like Me included a drunken priest whose faith is restored by Daisy revealing herself to be a Reaper.
This is an ongoing issue for Scully of The X-Files. She was raised as a devout Catholic and already had a few issues reconciling her work as a scientist with her faith. When she joins the X-Files and paranormal events and aliens get thrown in, she struggles to strike a balance.
Combat Hospital explores this one pretty thoroughly through an army chaplain who undergoes a crisis of faith as she serves in Afghanistan and sees the brutality of war up close and personal.
An All in the Family episode has Edith undergo one of these after Mike and a family friend are mugged on Christmas Eve, with the friend subsequently dying. Ironically, it's Mike who convinces her to reconsider.
A recurring problem for Adam Smallbone on Rev. According to his wife, it happens at least once a year. One particularly bad crisis sends him into a deep depression, lashing out at several people around him.
On one episode of Star Trek: Voyager, Neelix experiences a deep crisis of faith after dying, and being revived 18 hours later, without having experienced the afterlife his faith promised. After trying to come to terms with it, he tries teleporting himself into space to die, convinced that there really is nothing after death, but Chakotay manages to talk him out of it. The episode ends without giving a firm answer about his beliefs one way or another.
Drop the Dead Donkey has it both ways. In order to impress Japanese investors and Sir Royston, a debate between an atheist sociologist and a Catholic bishop is planned. Unfortunately, before it can go ahead, the TV news screens a piece of footage from the Middle East. The bishop is distressed in the inhumanity of it all, particularly when focusing on civilians caught up in the middle of violence, and loses his faith. However, the sociologist sees the same woman and same child and gains faith from seeing human survival against the odds and concludes the world must be in the hands of a divine being. The debate is, naturally enough, cancelled.
Brutaka from BIONICLE performed a brief but notable Face-Heel Turn when he lost his faith in the Great Spirit Mata Nui. Little did he know that Mata Nui's actually a very Physical God, who hasn't shown any sign of himself due to being in a coma. He later realizes that being a villain stands against all the other things he believed in, and the rest of the story portrays him as a mostly positive character.
In the play Doubt, Sister Aloysis experiences a crisis of faith after seeing the abuses of trust and privilege in the church. It's not a major plot arc but is significant because the character is a nun.
In the webcomic It's Walky!, a distraught Joyce, unable to reconcile her Fundamentalist beliefs with the events of her life shouts out at the heavens, then in a fit of inspiration (or insanity, or both) takes up the Power Booster Rod and goes out to seek out God for answers... or rather, the nearest equivalent, the immortal being known as The Traveler (AKA The Cheese), who is completely dumbfounded that she would think he could give her an answer.
The Simpsons has had a couple. For example, in "Homer The Heretic", Homer decides going to church is too much effort, and starts his own religion. Then his house catches fire, and he's rescued by Ned Flanders and a multi-faith volunteer fire brigade.
Reverend Lovejoy: Homer, God didn't burn your house down. But he was working in the hearts of your friends and neighbours, be they Christian [gestures to Flanders], Jew [gestures to Krusty], or [pauses] ...miscellaneous!
Apu: Hindu! There are seven hundred million of us!
Reverend Lovejoy: Aw, that's super!
Ned Flanders himself has a brief crisis of faith when his house is destroyed by a tornado (in a clear homage to the Book of Job, mentioned above) and then again with the death of his wife Maude.
South Park: Kyle loses his belief in God after Cartman gets a million dollar inheritance and buys his own theme park, while Kyle gets diagnosed with hemorrhoids. His faith is restored when he sees Cartman lose all his money, which Stan interprets was The Plan by God to punish Cartman the whole time.
Another episode has all the Catholics in South Park (which is pretty much everybody) declare themselves Hollywood Atheists due to the Pedophile Priest controversy. They wind up reverting back after Priest Maxi makes a televised speech to the church hierarchy about not letting unnecessary bureaucracy and corrupt rules get in the way of religion's core message.
Inverted in Justice League, "The Terror Beyond", with Hawkgirl questioning her own Naytheism. She's genuinely surprised to learn that Wonder Woman gets stronger by asking the gods for aid, and admits at the end that she doesn't understand why a teammate (who believed in an afterlife) was able to Go Out with a Smile. The episode ends with this subplot deliberately left hanging.
One episode of Daria has Quinn take a sudden interest in stories of angels, and she becomes convinced she has her own guardian angel when she happens to move just in time to avoid a dangerous accident. The problem is she comes to believe her angel will help her with everything, and becomes convinced that he's "abandoned" her when she embarrasses herself at a party. Daria puts aside her own feelings about the matter and helps Quinn decide she should only trust her angel for "big" issues.