The Spelunker from Spelunky, being kind of an Indiana Jones expy hates snakes, too. Doesn't really seem to stop him, though.
World of Warcraft has a shout out in the form of an NPC with a strong fear of snakes who's named Harrison Jones, which takes Indy's last name and his actor's first name.
The last line of a journal entry in Vesuvia that mentioned the discovery of a charred snakeskin was "Snakes - anything but snakes..."
Gemini Man from Mega Man 3 hates snakes. Not surprisingly, he takes massive damage from Snake Man's Search Snakes.
Part of a certain side quest chain in The Lord of the Rings Online involves retrieving some baby turtles from the work shed of a hobbit named Grobo Dogroot who just so happens to be deathly afraid of turtles. When you go to pick up the little suckers, each and every one is called "Grobo's Greatest Fear."
In Lego Indiana Jones, several puzzles revolve around Indy's fear of snakes. You have to get rid of the snakes with another character (and it's not as easy as attacking them, since they're often in deadly mud) so Indy will join you where his skills are needed.
Ryoh from Warbears, to the point where he climbs out of a window and across a ledge, then through another window to avoid a spider.
Various spirits from Ghost Master specialize in exploiting certain fears; one of them in a giant spider.
One of the quests that you can do in Stormreach Harbor in Dungeons & Dragons Online involves a guy named Berne Jorn who's been afraid of spiders ever since he was a kid. The quest he sends you on, which is called "Arachnophobia," has you clearing the eight-legged bastards (including a huge boss-level one) out of his family crypt.
Toonstruck's Drew Blank exclaims "Spiders! Why did it have to be spiders?" upon seeing a couple of them crawling on the wall.
Bounder Boffin of The Lord of the Rings Online is terrified of spiders, which you have to kill during the introductory instance for Hobbits in order to help him cut through Old Odo's Leaf-farm to escape a Black Rider.
Farkas, an otherwise fearless warrior of Jorrvaskr in The Elder Scrolls V: Skyrim, at one point refuses to go any further in the Tomb of Ysgramor after encountering giant spiders there due to his experience with them back in Dustman's Cairn.
Kormac from Diablo III does not like spiders. At all.
Adelbert Steiner in Final Fantasy IX, sort of. He's deathly afraid of oglops, an otherwise harmless insect. So is Blank, though not to the same degree (he says he "can't stand them", but is able to put up with them for the sake of the plan to kidnap the princess). Though when Blank's armour breaks and the oglops are released, both Steiner and Blank begin running around in a panic. Garnet/Dagger later fakes a fear of oglops in order to make her "ordinary girl" act more convincing.
Blathers the Owl from Animal Crossing hates bugs of all sorts, as made obvious by how he reacts every time you turn in something for the museum's bug collection.
Lyle Smithsonian of Metroid: Other M really hates bugs. Guess what's invaded the Bottle Ship?
Florina from Fire Emblem 7 is terrified by bugs (a support conversation shows her panicking when a bee flies around her), among a few other things.
Karol in Tales of Vesperia is shown to be petrified of them when the party visits a forest teeming with insects. In a rare show of kindness, Rita gives him a can of bug spray, which becomes a skill called 'Bug Busters' for him.
The eponymous Pikmin flee in terror from otherwise harmless Mitites.
Mice and Rats (musophobia)
The Good Fairy in Ceville. Obviously you have to exploit her weakness to solve a puzzle.
Zelda from The Legend of Zelda: Spirit Tracks doesn't like mice. Used as a gameplay as Link has to get rid of those rodents before she will move on. Understandably it comes up as the third part of the final boss fight where if she gets touched by one, she fall under Cole's control. This creates the amusing sight of an imposing suit of Animated Armor (which Zelda possesses) shivering in fear at the sight of a mouse.
The title character in Nick Chase and the Deadly Diamonds announced at one point that rats were his one weakness, his Achilles' heel.
Metal Gear: Naked Snake has a fear of bats, and (by extension?) Dracula.
Serge from Chrono Cross was said to have this (though he's apparently grown out of it by the time the player controls him). Justified in that he was attacked and nearly killed by a panther demon as a small child. We learn later that Serge's father, Wazuki, was turned into a cat-like form by FATE because that was the thing that Serge feared the most.
A short time into the events of Geist, it is revealed that Big Bad Volks's Dragon Rourke is afraid of dogs. Close to the end of the game, Volks holds a meeting behind locked doors and gives specific orders to shoot anyone who comes close who isn't himself or Rourke. The solution is straightforward: possess Rourke. To possess someone, you must first terrify him. Thus, you undergo a series of short missions for the sole purpose of getting a dog into the same room as him.
Alessa Gilespe from Silent Hill was terrified of dogs, which due to her and the town itself being a Reality Warper who brings fears and abstract concepts to "life" is responsible for several monsters you see throughout the series; Split Head, Groaner, and possibly the Caliban.
According to the Drama CD of Guilty Gear XX, Zappa is terrified of dogs (then again, he seems to be scared of everything). Guess what? One of the ghosts possessing him takes the form of a huge, hulking black dog.
Frederick from Fire Emblem Awakening is afraid of wolves due to nearly getting killed by one when he was younger. Even something that looks like a wolf, like a taguel, can trigger this.
Tron Bonne, from Mega Man Legends, is afraid of dogs and was once chased up a street lamp by a dog.
Frogs & Toads (batrachophobia)
Lucca of Chrono Trigger. Becomes awkward when it comes up immediately after they meet with one of the party members, a giant anthropomorphic frog.
Refia of Final Fantasy III has a fear of frogs, which makes for a fairly amusing conversation the two times where you have to transform into one to enter a dungeon. It's even better if she is the character who has to cast the "Toad" magic.
Volgin from Metal Gear Solid 3. The phobia is so strong that if you toss a live frog at him during your boss fight with him, he'll stop attacking you to kill the frog, allowing you to get a hit in.
Cornet of Rhapsody A Musical Adventure suffers from this. Unfortunately, frogs are hiding in every other container in the Marl Kingdom. Oh, and there's a kingdom of bipedal, sentient frogs.
Slugs & Snails (molluscophobia)
Ursula of Breath of Fire IV is utterly terrified of sea lice (a harmless bug). Especially hilarious as this ends up being revealed in a "What Do They Fear?" Episode segment between her and Nina, and Ursula is normally a Type A Tsundere who tries to be tougher than most men...
All playable lawyers, save Mia Fey seem to suffer from this in the Ace Attorney series: Miles Edgeworth (who already has a Seismophobia to boot) needs Gumshoe to fetch him books from the higher up shelves, Phoenix Wright has to be led by his hand by his teenage sidekick when passing a bridge and breaks out into hysterical catchphrase-shouting upon boarding a Ferris Wheel and Apollo Justice can't ascend as much as 10 meters without starting to shiver like a dry pile of leaves.
Alister, Lara Croft's Non-Action Guy partner from the Tomb Raider series, does not like heights. At all. They make him "positively nauseous," as he comments at one point in the Japan mission of Tomb Raider Legend where Lara is making a dangerous climb up a really tall office building.
Blaze the Cat from the Sonic Rush series is often implied to have a fear of heights, especially when they reach a zone like Sky Babylon.
Emma, Hal's sister in Metal Gear Solid 2 doesn't like heights when asked about it by Raiden, but stated it's preferable to Water.
Bartz Klauser in Final Fantasy V has a fear of heights ever since he almost fell down from the roof of a two story house while playing hide and go seek. He reveals this the first time the party rides the wind drake, and Galuf physically hurls him onto its back. Later on, he hesitates before jumping off the relatively low height of Bal's drawbridge into the moat.
As part of its many Call Backs to earlier Final Fantasy games, Vivi Orunitia from Final Fantasy IX, just like Bartz, has a fear of heights stemming from falling from a great height when he was young (specifically falling out of the cargo ship.)
Chrono Trigger has the example of Golem Boss who, after Dalton summons on top of the wing of an airship, cowers in fear from the height, without attacking. If not killed quickly, he then runs away.
In one mission in Grand Theft Auto IV, Niko seems nervous about having to take a lift on the outside of a building to get to its roof. And in San Andreas, Cesar refuses to get into a crane because he's afraid of heights.
Sonic the Hedgehog displays a fear of water in some adaptations (such as Sonic X, for instance), though not actually in the games.
Lesley Lopicana in Mitsumete Knight, a Spiritual Successor of Tokimeki Memorial. She's an Expy of Ayako, but unlike her where the origins of her fear were never explained, we get to know how Lesley got this fear of water (long short story - that you can read in the game's Character Sheet, - it's due to a Childhood Trauma).
The dragon in Loom is afraid of fire, a fact Bobbin uses against her with either the Terror or Sleep draft to set her hoard — transformed by him from gold into straw — ablaze.
It's hinted that Milla Vodello of Psychonauts is a pyrophobe due to the orphanage where she worked burning down with the children inside it.
Heather in Silent Hill 3 is afraid of fire. She comments that "it's scary somehow..."
Other nature phobias
One of the player characters, Rikku from Final Fantasy X has a phobia of lightning (astraphobia), which she gets over in the sequel.
Earthquakes (seismophobia) — Miles Edgeworth from Phoenix Wright: Ace Attorney. The first major crack we see in Edgeworth's stoic facade is that he turns into an absolute mess at the slightest of tremors. It's no better in Trials and Tribulations, when he passes out after an earthquake hits Hazakurain. It also extends to airplane turbulence (which can resemble tremors) and elevators. Justified in it being the result of a traumatic and tragic incident he experienced as a kid.
Jonathan Ingram in Policenauts is a cosmophobe by his own admission, and also appears to show some level of claustrophobia. This clearly doesn't work in his favour when he has to leave the Moon via a material transport relay. Depending on the players' responses to Ed, and how long it takes the player to make the decision to leave, it will extend the action sequence. The first time you beg Jonathan to enter the pod, he will refuse.
Timbersaw from Dota 2 has a severe fear of trees, to the point that he built a mechanized suit for the purpose of cutting them down.
Barry Dejay in Backyard Sports. He plays worse on the Bling-Bling Brothers Circus in Backyard Basketball just because he is afraid of clowns.
The players of City of Heroes often ask for a Clowns powerset for the Mastermind (pet summing class based on minion-commanding villains), but are denied because Matt "Positron" Miller, the lead developer, is afraid of clowns.
Nathan Drake from the Uncharted series. At the end of Uncharted 2: Among Thieves, Elena asks him on a scale of 1 to 10 how scared he was that she would die, he gives it a 3 or 4. Guess what was at 10?
Trevor Philips from Grand Theft Auto V hates clowns, which unfortunately are what he sees after sampling someone's marijuana.
Lon'qu from Fire Emblem Awakening, which stems from his guilt of feeling responsible for the death of a childhood friend. He'll eventually make an exception for whichever female you decide to pair him with (and his daughter, should he have one).
Yoshi is afraid of ghost houses, so he stays out of them while Mario and Luigi explore them. In spite of this, two bosses in Yoshis Island and one in the remake are ghosts. Also in both games, one Yoshi's relay leg consists entirely of fortresses while another has all castles.
Yukari Takeba from Persona 3 is also afraid of ghosts.
Metal Gear Solid 3: Snake Eater: Naked Snake is terrified of anything involving the undead. Bats make him think of Dracula, and merely mentioning Dracula is enough to give him nightmares. Because Hideo Kojima loves to screw with his own character's minds, Naked Snake gets to face the ghosts of every person he's ever killed in the game. It's a little unsettling for us, the players, but it's horrific for him. In Peace Walker, there are more ghosts in some bonus levels. When Chico, a fan of cryptozoology, starts describing an optional boss as an "undead dinosaur" brought back to life by Haitian zombie-makers, Snake's phobias kick right back in and he starts trying to rationalize it as just an "ordinary" dinosaur that happens to be skeletal and immune to conventional weapons.
Ragna the Bloodedge's Joke Ending in BlazBlue: Continuum Shift reveals that he is terrified of ghosts. So his joke ending turns him and most of the cast into ghosts. It's canon too; he is freaked out by Sena, one of the personalities that make up Platinum the Trinity, when Sena threatens to haunt him for the rest of his life in an attempt to mooch a meal off of Ragna. To top it all off, the true form of the Big Bad Terumi is a creepy grinning green ghost.
Princess Pitts in Chibi-Robo possesses a lady-like terror of monsters and the like. As Chibi-Robo, you can use a Ghost suit to help train her to overcome her fear, though it takes a while and she faints a couple times initially.
Judging from what she says about the Old Chateau (a place where Ghost Pokemon and actual ghosts lurk), Gardenia, the Eterna City Gym Leader from Pokemon Diamond And Pearl has this phobia. (Oddly enough, if you challenge her with actual Ghost Pokemon on your team, it doesn't make any difference.)
Alan Wake: Alice has a crippling fear of the dark. And don't tell me you didn't flip on a few lights yourself after/while playing through the game.
Daniel from Amnesia: The Dark Descent has a bad fear of the dark after an incident from his childhood. Staying in the dark too long makes his sanity lower and causes hallucinations, blurred vision, and teeth grinding. Too bad they didn't have very good lighting in 1839.
Porcelain (porcophobia?) — Guybrush Threepwood. Speculated to have been caused by being hit over the head with a porcelain vase in the first game. The developers have said they added this just as a gag - after all, who is scared of porcelain? Referenced in Tales of Monkey Island Episode 1: Launch Of The Screaming Narwhal, when you have to pick up a porcelain action figure. Guybrush grits his teeth and reassures himself "Calm down, Guybrush, it's only a little porcelain..."
AGAIN Emma Emmerich shows up on this list: she doesn't like sea lice at all. We also have Big Boss himself, scared of vampires and zombies. This is a subversion in terms of the 'recurring obstacle' trope - vampires are in the series (in aform, anyway), but Big Boss never encounters one.
Bald people: May of Guilty Gear has an extreme fear of bald men, and can even sense when someone is bald, as shown during the Story Mode in XX when she runs into Dr. Faust (who, under the paper bag, is bald).
Battler Ushiromiya is terrified of any vehicle that shakes when it moves, as was his late mother Asumu.
Flora, Layton's ward in the Professor Layton games, is afraid of being left alone (monophobia).
Artix, normally fearless paladin extraordinaire in AdventureQuest Worlds, is utterly terrified of the color pink (which Beleen mercilessly teases him about).
All dwarves in Dragon Age (apart from those born on the surface, obviously) tend to have some fear of the sky (possibly Agoraphobia or Ouranophobia) due to the vast majority of them living in underground cities. They fear that going to the surface will not only make them lose their 'stone sense', but that they will fall up into the sky (this is called Casadastraphobia). Of the three dwarves you can recruit, one is a surfacer anyway, and the other two overcome their discomfort fairly quickly. Anders the mage appears to have claustrophobia, given his comments whenever you venture to the Deep Roads in Dragon Age: Origins – Awakening and Dragon Age II. There are also plenty of people who are terrified of mages/magic/demons, and of those, plenty are justified.
In Ib, Garry is utterly freaked out by all the blue dolls. Can't blame him considering one of them stalked him down a hallway and there was another time where a whole bunch of them captured him and forced him to play a game with them, but he found them disturbing even before any of them did anything.
In addition to fearing sexy women (see above), Laharl is also horrified by declarations of love and positive thinking. He's mostly over it by the end of the game.
Parodied in Deadfall Adventures, where James Lee Quatermain's nonhuman archnemesis is... math. Naturally, he comes across not one, but two puzzles involving math — in the Mayan numeral system, no less.