In My Little Pony: Friendship Is Magic Fanfic Progress, Princess Luna ends up mortified of baseballs after getting hit in the face by every last foul ball in a baseball game due to a spell gone hilariously wrong. Some time later, she watched Cupcakesnote An infamous Dark Fic about Pinkie Pie brutally torturing, murdering and baking Rainbow Dash on tv, and becomes terrified of all things pink as well. Though she manages to get over that one in time to hang with Pinkie Pie later.
Similar to the above, Delilah from The Legend of Spyro: A New Dawn is deathly afraid of cupcakes after the "Cupcakes Incident", which apparently involved a run in with the Cupcakes version of Pinkie Pie (Delilah is a Dimensional Traveller). Though it doesn't come up in that fanfic, since cupcakes don't exist in the universe it takes place in, a letter she gets from Pinkie Pie (the real one, who she's best friends with) tells her to call ahead before she visits so her friends won't have them at a surprise party due to her phobia.
Rarity's character arc in the Pony POV Series involves getting over the phobia of gems she'd gotten from Discord's Mind Rape of her. Many other ponies throughout Equestria got similar phobias as a result of their own Mind Rapes, including Prince Blueblood being terrified of the sun, Big Macintosh is terrified of the family dog, Sweetie Belle is scared of her dolls, etc.
The One and OnlyTrixie is revealed to have a crippling fear of Ursas after the Ursa Minor incident in Ponyville. This, rather embarrassingly, rears its head when they encounter two cute, teddybear-sized ones who'd be "fixed" by Princess Gaia's Reality Warping. It scares her so badly that it takes Pinkie Pie singing her a rendition of "Giggle At The Ghosties" to calm her down. Understandably, the others don't laugh or mock her about it, as they know and understand why it scares her so badly.
In Renegade, Shepard has a specific fear of the alien Scrin, and for good reason: she's the sole survivor of the Scrin assault on Akuze, and got an up-close and personal encounter with Buzzers that left her horribly scarred. When the Scrin attack the GDI Embassy on the Citadel, her reaction to close-quarters combat is to go from her normally controlled and unflappable demeanor to shouting and screaming at them.
There's a whole assortment of fears in Never Fear the Shadows. Harry's dad was afraid of water, his mother of clowns, Remus of moths and Sirius of being locked up, while Harry himself was afraid of loud noises, with good reason.
It's speculated by some that whoever's running The Infinite Loops deliberately invoke this trope for some reason. In universe, it's probably to help treat Anchors so they aren't as metaphysically unstable. Out of universe, it's just hilarious.
The RWBY Loops have the loopers of Remnant mildly terrified of bunnies, though how much is actual fear and how much is pretending to be afraid for fun is somewhat debatable. Notably, Blake takes the time to list off all the rabbits and hares in the multiverse that could be considered dangerous, justifying their reactions.
In Boys Und Senshado, as a result of his father's death in a landing accident, Akio starts hyperventilating when he even gets on a plane, which essentially makes it impossible for him to do Sentoki-do, the dogfighting sport the rest of his family does.
In Takamachi Nanoha Of 2814, Nanoha is utterly terrified of Evangeline (then again, everybody from the Magic Side is terrified of her) and Godzilla (since Japanese pop culture ingrained into her the fact that Godzilla cannot be defeated).
The main character of The Twilight Child is unnerved by Timberwolves after a childhood friend of hers was nearly killed by a pack of them during a camping trip gone wrong. She's also incredibly twitchy around deserts, due to nearly dying from dehydration in one twice, to the extent that she gets nervous when a few miles away from one, or even being outside when it's incredibly warm.
In a Played for Laughs version, Rarity is deathly afraid of cheese. She refuses to explain why, but it's implied she was tormented with it by a rival. Somehow.
A Voice Among the Strangers has Jessica develop a phobia of unicorns and their magic, after being captured and caged like an animal by the Flim Flam brothers for a week. However, she manages to largely get over it by the end of the second chapter, thanks to the friendship of Dinky and Twilight.
Returning is a Harry Potter fanfic where one of the first-year characters is scared of flying. At Hogwarts. Where flying lessons are compulsory.
On top of her pediophobia from canon, Asuka has pharmacophobia in Advice and Trust due to her step-mother drugging her with emotional suppressants when she was young. She almost had a panic attack when she discovered that Rei had been placed on similar drugs.
In both Shadow of the Dragon and Be Careful What You Wish For, Lord Archive is noted to elevate Sakura's Phantasmophobia into Thanatophobia. She hates death so much, especially it's abruptness, she's willing to fight fate; something CLAMP has mentioned to be a bad idea.
In Dodging Prison and Stealing Witches due to over a decade in Azkaban in the previous timeline, Harry is terrified of being locked up. Any time he's "trapped", he starts immediately panicking and at one point destroys an entire classroom during a meltdown. This is especially problematic as Harry doesn't always think things through and ends up in ambushes where he needs to think clearly but can't.
In This Bites!: Enel's Electric Torture has left Cross with a case of astraphobia, making him flinch whenever he sees as much as a flash of lightning. Chapter 37 reveals that Chopper's therapy has almost completely eroded it.
In Loki's Family Odin is afraid of spiders due to a prank played by Freya.
In The Lover's Left Broken, Sara, badass assassin Sara, is terrified of...pregnancy. When she learns Laurel is pregnant, she tries to read up on it to help, but becomes steadily more grossed-out/horrified by it, to Laurel's amusement.
Sara: There's a real living thing growing inside of her basically stealing nutrients from her body and making her sick and tired and - I'm sorry, did you know that a woman's organs literally shift during pregnancy? Laurel has a parasite inside of her body that is moving her insides around. (shudders) Ugh.
In the main story, Misty is afraid of bugs just like in canon, but she also develops a phobia of Vileplume when she ends up covered in the spores of one, almost dying as a result. Oddly enough, she's not afraid of Gyarados, although it's unclear if she already conquered that fear or never had it in the first place.
A sidestory focused on Gardenia runs on the interpretation that she really doesn't like ghosts and Ghost-type Pokémon, but when her friend Cheryl gets lost inside the Old Chateau, she braves her fears to find her.
In Syngenesophobia, Lincoln Loud develops a crippling fear of his sisters note Lily is the only Loud sister Lincoln isn't afraid of. after they gang up on him during Brawl in the Family.
Flying (aviophobia) or Heights (acrophobia)
In Finding Dad, Isabella is afraid of heights. Luckily, Phineas is there to comfort her.