Snakes (especially the enormous constrictors that always crop up in Robert E. Howard's stories) are the only thing that Conan the Barbarian is afraid of, besides some displays of sorcery. The ancient god Set, the embodiment of evil in Howard's stories, is represented as a serpent.
The Conan RPG system has the spell "Dance of the Cobras", which is Exactly What It Says on the Tin. Cobras are hypnotized to circle a person, doing damage each round until the victim either dies from the damage or kills all four of the cobras, which are specified as at least Medium size. The spell comes from the Conan story "The Man-Eaters of Zamboula," which had Evil Sorcerer Totrasmek doing this to the Love Interest Zabibi, who is forced to dance for her life against the snakes.
Kahlan, the primary female character of the Sword of Truth, hates snakes. She becomes highly nervous and uneasy when Richard mentions he saw snakes in the water, later has nightmares about a large snake wrapping around her legs. Her aversion to snakes is mentioned several times again over the course of the series. This is a fairly common syndrome among female characters from this series.
Josh Newman from The Secrets of the Immortal Nicholas Flamel is revealed to be afraid of snakes. He lampshades it in The Sorceress - "Snakes! Why is there always snakes?" He even says the trope name in The Magician.
Hank the Cowdog from the series of the same name can face bobcats, coyotes, mad bulls, and wild horses (although he'd much rather not). Snakes are the only thing he's specifically named as terrifying him.
Silk, from the Belgariad, is a victim of this. He also has a fear of caves.
Ron Weasley of the Harry Potter series is deathly afraid of spiders, due to his brothers transmogrifying his teddy bear into a massive spider for a joke when he was much younger. During Harry Potter and the Chamber of Secrets, he and Harry end up having to "follow the spiders" into the Forbidden Forest. In the movie version, Ron quips "Why spiders? Why couldn't it be 'follow the butterflies'?"
In a fortuitous bit of casting, Rupert Grint, who plays Ron in the movies, is also deathly afraid of spiders. All of "Ron"'s expressions of fear in the movies are actually those of Rupert, since, according to the DVD special features, Aragog was animatronic. (Aragog's children, however, were CGI.)
"Ayatollah", the crime boss in Boris Strugatsky's The Powerless of This World, fears nothing except members of the class Arachnida. Unfortunately for him, one of the friends of his victim is commonly known as "Beelzebub, Lord of the Flies" for his amazing ability to control insects and spiders...
Giant spiders show up a lot in Tolkien's works, especially in The Hobbit and The Lord of the Rings. Among all other creatures in Middle-earth, nothing strikes more fear in the characters — especially the hobbits — than spiders (except for maybe the Balrog, which only scared the characters who knew what it was). Some people believe this stems from Tolkien having been bitten by a tarantula as a very small child, but he adamantly denied this in life.
The annotated edition of The Hobbit has a quote from Tolkien, in which he claims that he put the spiders in because he knew his son was terrified of them.
Peter Jackson also shared this fear, which he used during the film version of The Return of the King to make the scenes with Shelob as nightmarish as possible. He told the people in charge of CGI for the scene to keep enhancing things "until [he] couldn't stand it."
Nicci of the Sword of Truth suffers from a fear of lice (pediculophobia), as a result of being repeatedly infested with them during her childhood in the Old World. Upon seeing a young girl who has a lice problem, she forcibly cuts the girl's hair and washes her head, then instructs her to burn her clothing and bedding.
Private detective Bobby Dakota, in Dean Koontz's The Bad Place, fears insects of all kinds.
The Star Wars Expanded Universe gives us the Dark Nest Trilogy, about...bugs from Alderaan. If you're around these bugs for a long enough time, you join their hive mind. Han and Leia's daughter Jaina, her boyfriend Zekk, and Luke's son Ben do so. Han Solo says "Bugs, why did it have to be bugs?"
In Galaxy of Fear, Zak Arranda has a definite aversion to large insects, which really bites him in The Swarm, which takes place on a world where the local people are giant bugs and the main threat is... smaller but still large bugs.
Mice & Rats (musophobia)
Cara, another supporting character of Sword of Truth, has a fear of rats. Author Terry Goodkind appears to like giving his female characters different phobias.
John Rambo in First Blood. While having no problem with surviving in the wild and killing in self-defense, he clearly can't stand being surrounded by rats while hiding in a cave.
In Indiana Jones and the Last Crusade, it's revealed that Indy's dad is afraid of rats. (He says so when he encounters a horde of them in the Italian catacombs, and it is confirmed when he tells his father about it, causing the elder Jones to tremble in fear.)
Winston Smith of 1984, which the Party uses as his personal, tailored torture in Room 101.
In The String of Pearls, the original story of Sweeney Todd, Sweeney is terrified of dogs. Unfortunately for him, Mark Ingestrie's dog Hector is rather persistent.
In The Gray Chronicles, Gray has a crippling fear of dogs. This is initially Played for Laughs as he's fearless when facing demons, monsters, and angry ghosts that are far more dangerous than a barking chihuahua. Then The Rival sent his vicious attack dog after him and it became outright horror. Later subverted when Gray takes in an injured puppy out of kindness and realizes not all dogs are evil. (He still names the tiny Scottie BLOODFANG THE DESTROYER!, but it's tongue in cheek, especially since the dog's the runt of his litter.)
In Stephen King's novel IT, the frightening forms IT takes on, drawn from the personal fears of its victims, include giant birds in several cases, though IT is usually more remembered as a Monster Clown.
One character's fear of a giant bird is revealed later in the book to originate from being attacked by a normal-sized bird when an infant. The other does not fear birds per se, but the impossible dimensions of this one in particular, a species that does not and cannot exist in the real world.
Also shows up in the Neil Gaiman novel Anansi Boys, although is it an irrational fear when the birds really are out to get you?
A minor character from Harry Potter and the Chamber of Secrets, Mrs. Mason, is terrified of all kinds of birds, so when an owl flies in to warn Harry about using magic.... well, let's just say Uncle Vernon didn't get the big paycheck he wanted. Likewise, Harry gets locked in his room for the remainder of the summer.
Flying (aviophobia) or Heights (acrophobia)
Most of J. R. R. Tolkien's hobbits are stated to be uneasy if they are any distance off the ground, this perhaps being one of the reasons why they live in "hobbit-holes" and one-story houses.
Tortall Universe: Keladry of Mindelan is terrified of heights after being held over the edge of a tower by her brother. It mostly goes away at the end of the second book, but never completely.
Jack Ryan not only lost both of his parents to an airliner crash, but early in his (aborted) military service the helicopter he was riding in, for an exercise, crashed, leaving him needing significant surgery, and ultimately having a fear of flying. He eventually got over it later in the Ryanverse series, though.
Percy Jackson in Percy Jackson and the Olympians is scared of heights. Justified in that he is a son of Poseidon, and the sky is part of the sphere of influence belonging to Zeus. The only exception is with Pegasi, because Poseidon created horses, which means that they are neutral territory.
Ironically, Thalia is deathly afraid of heights, despite being the daughter of Zeus.
Word of God also says that children of Hephaestus are afraid of heights and falling, because when he was born, their father was chucked off Olympus by Hera.
In Discworld novels, Rincewind was always afraid of heights, so during his adventures he often ends up hanging or falling from high places. In Interesting Times his friend, Twoflower, reminisces about the "good old times":
Twoflover: Hey, do you remember the time when we went over the edge of the world? Rincewind: Often. Usually around 3 AM Twoflover: And that time we were on a dragon and it disappeared in mid-air? Rincewind: You know, sometimes a whole hour will go by when I don't remember that.
Actually, when he was on a boat, Rincewind clarified that it wasn't so much heights he feared as depths, which included large bodies of water. Anything where you could fall for a considerable distance, ending in death.
Anthony Horowitz's Scorpia has this for the book's Dragon, Nile, as his only weakness, the only thing that made him finish second at the training camp for the book's eponymous Murder, Inc.. It's also what leads to his death: under orders from his boss, he confronts Alex on a hot air balloon. Alex points out the height long enough for him to lose his focus, and a quick trick has him fall off.
In Terry Pratchett's The Colour of Magic, we meet dedicated "hydrophobes", who are raised with a deathly fear — indeed, loathing (not hate, which is the opposite side of love) of water. This fear is so strong that they can pilot a hovering board over the ocean, since their aversion to water forces it away from them. Unfortunately most of them end up dying early, overcome with revulsion over the water in their own bodies.
David Eddings features one particular character in the Belgariad/Malloreon series: Queen Layla of Sendaria. She has not so much aquaphobia but a specific form of megalophobia (fear of large objects): she is terrified of ships (more specifically, ships sinking), to the point that she can actually faint if a ship moves the wrong way.
Oddly enough, Data, the android of Star Trek TNG fame, gained a fear of water during the novelisation Metamorphosis in which he was turned human. (Yeah, it's that kind of book.) This fear is absent from the series. Probably because he can't, you know, actually drown (though the few encounters he has had with water lead to him sinking abruptly to the bottom due to his heavy weight, and having to spend several weeks draining out his servos.)
Stephen Dedalus in Joyce's Ulysses is mentioned to be a hydrophobe, although this is probably symbolic of his antipathy toward baptism/Catholicism.
Jayfeather from Warrior Cats is afraid of water. However, he manages to get over it in Night Whispers.
Johanna Mason from The Hunger Games trilogy develops this in the third book, after the Capitol uses water (combined with electricity) to torture her.
Hazel from The Heroes of Olympus. Justified because it's Neptune's territory and she's the daughter of Pluto.
In Seanan McGuire's October Daye novel Rosemary and Rue, Toby panics when she lands in the ocean — since turning into a fish and recovering, she can't stand bodies of water.
Sandor Clegane, a.k.a. the Hound, in A Song of Ice and Fire. Quite a reasonable fear, as half of his face has been burned as a child by his evil older brother. He lives in a world with Greek Fire and priests of a fire-god who can, well, magically create fire, and naturally runs into both.
Harry Dresden of The Dresden Files, after his left hand is burned beyond use in Blood Rites, becomes reluctant to even attempt fire magic at all. He eventually overcomes his fears and concerns by the end of Dead Beat, though a villain in White Night mistakenly assumes he's still very afraid of fire and makes a failed assassination attempt based on that.
Torak from the Belgariad was terrified of fire. Kind of odd for a God to be terrified of anything unless one can see the future, as he can, and knows what's going to happen to him.
Throughout his appearances in the Discworld novels, Mr. Slant the (zombie) lawyer is almost completely fearless, even when dealing with sociopathic criminals. As a result of being a well-preserved (and by necessity, extremely dry) corpse however, he is terrified by fire.
In The Wonderful Wizard of Oz the Scarecrow reveals to Dorothy that a "lighted match" is the only thing he's afraid of. Although, given that he's made of straw, can you really blame him? In the movie, the Wicked Witch of the West exploits this fear on several occasions.
Wicked Witch of the West: How about a little fire, Scarecrow?
The titular monster from IT by Stephen King takes on the appearance of whatever its victims fear. One of IT's most well-known forms is that of a Monster Clown, though this image is not always immediately recognized as evil, and has been used to lure in young children. The clown in question is said to smell of boiled peanuts, cotton candy, animal dung, and rotting dead things.
The Dark (nyctophobia)
In The Wonderful Wizard of Oz, the Witch of the West was not only afraid of water, but also of the dark. This was why, even though Dorothy was her prisoner, she couldn't take the slippers from her; the Witch of the South's blessing prevented her from hurting Dorothy, and Dorothy only took them off herself when she slept and bathed, keeping the Witch at bay due to the two things she was afraid of.
The seemingly fearless John Carter of Mars tends to completely lose his shit when he's plunged into total darkness, and may even start hallucinating that he's being chased by monsters with burning eyes.
Fear itself (phobiaphobia) — Harry Potter seems to have it... well, sort of. (Well, to be specific, boggarts look like Dementors to him, and Dementors are living embodiments of fear.)
Going by the shape boggarts take, Hermione is afraid of flunking her classes (or maybe failure in general). She was so terrified of this, she wasn't able to use the Riddikulus spell to fight it.
Another example, Professor Lupin is afraid of the full moon. Justified because he's a werewolf.
In Tad Williams's Otherland, the head of J Corp. has his subordinates watch the sadistic execution of two failed employees, in which he uses virtual reality to subject them to death by the things they are most afraid of: in one case, drowning, in the other, injections.
The protagonist of Iain Banks's Use of Weapons has an odd phobia of chairs. It makes a lot of sense when you learn what the original chair was made of.
Throughout the Discworld series, Rincewind has developed a violent fear of many things, some justified (the Things of the Dungeon Dimensions), some not (having good things happen to him, because it usually means something worse is coming along later), but the thing he seems to dread the most is plots, because if a plot starts happening anywhere near him, eventually he will get sucked into it. Rincewind was afraid of playing football in Unseen Academicals, but then so was every other wizard except Ridcully.
Conan is also afraid of wizards and magic in general, which a common theme in stories about the character. (At the very least, he doesn't trust them.)
Ciaphas Cain (HERO OF THE IMPERIUM!) is secretly scared of a lot of things, but Necronsnote a sort of fusion of ancient unkillable evil spirits and killer robots scare him so much that it even shines through in his official hero persona; if he was as everyone thinks he is, they would be the only thing he fears. They are the one enemy he will not face in direct combat.
Several characters in Dean Koontz's False Memory have phobias. Susan Jagger is agoraphobic and fears leaving her house. Martie Rhodes is autophobic, meaning she's afraid of herself (specifically she's afraid that she might commit a violent act). And the nameless wife of an Internet billionaire is terribly afraid of Keanu Reeves; she can't look at pictures of him and can't watch television because she might see a commercial for one of his movies.
The closest to karmic retributionThe Talented Mister Ripley receives is that he develops a fear of cops for the rest of his life. He can never look at another cop again without a brief flash of alarm as he thinks that the cop has discovered his crimes.
Dan Brown's Robert Langdon is severely claustrophobic as a result of almost drowning in a well as a child. He regularly has to enter confined spaces in the novels, including being imprisoned in a coffin in Angels and Demons and actually faces drowning in tiny space in The Lost Symbol it turns out to be a total liquid ventilation system, but he didn't know that.
Rachel Creed in Pet Sematary suffers from serious necrophobia (fear of death). She can't even handle hearing the concept mentioned in her presence without freaking out.
Adventure Hunters: Lisa is terrified of gargoyles because of a bad encounter with them in her childhood.
October Daye, a very high-powered bloodworker, is badly thrown by the sight of her own blood (autohemophobia?).
In Peter Pan, Captain Hook was similarly afflicted. It was said that the only thing he shied at was the sight of his own blood, which was thick and of an unusual colour.
The Nome King who first appeared in Ozma of Oz is afraid of eggs, but he has a very good reason - they are poison to his species. (What they can do to them varies depending on what book you read, and is inconsistent, anything from make them sick to reduce them to dust.) This makes him incredibly terrified in one book, when a barrage of Baleful Polymorphs gone out of control turns the whole cast into animals, turning him into a goose; he's afraid of birds too, because birds lay eggs, and he has no idea what might happen if he laid an egg while turned into a bird!