One episode of Kim Possible parodies Indy's fear. When Kim arrives in a spiked pit while searching an abandoned underground temple, she jokingly asks, "Where are the snakes?" When hundreds suddenly appear, she retorts, "I was just being sarcastic!"
Also parodied in at least one Tomb Raider comic. "I met this man once who would have been a good archaeologist, but he just couldn't get over his fear of snakes..."
Launchpad also parodies it in the Five-Episode Pilot of DuckTales: "Yah, a snake! I hate snakes! No... that's somebody else. I sorta like snakes." Then one nearly eats him: "Now I hate snakes."
Pee Wee Herman (snakes), at least in Pee Wees Big Adventure, when he rescues them last from a burning pet shop.
In Jackass: Number Two, the gang does a bit where they trap Bam Margera in the back of a trailer with a (devenomized) king cobra. Hilarity Ensues when Bam goes apeshit and actually starts crying.
It gets worse in Jackass 3D: They set Bam up to do a prank... but are really sending him directly into a trap door that leads into a pit full of rubber snakes. Bam flips his shit. Then they add in REAL snakes, including a giant yellow one, and he proceeds to frantically hold on to the side of the pit, trying to pull himself out.
Suki in The Scribbler is using an experimental electroshock therapy to cure her Split Personality syndrome. One of the side effects is blackouts; after one such blackout, she wakes up on the ground outside her apartment complex, being harassed by the building's security guard. Luckily, her Bourgeois Bohemian neighbor - who goes nowhere without her pet boa constrictor draped over her shoulders - comes to the rescue, scaring the guard away with said snake.
The protagonist of Arachnophobia, a doctor who moves his family to a small town to escape the dangers of big-city life, only to come up against an invasion of deadly hybrid jungle spiders.
Ichabod Crane in Sleepy Hollow can handle grisly autopsies... but sees a (admittedly large) spider in his room and leaps onto a chair, yelling, "Kill it! No, stomp it!"
Jovanovich, the big tough mob leader in Jungle 2 Jungle, freaks out when he sees a big spider on his head in the mirror, even shouting, "I hate spiders!".
James Bond has an understandably harsh reaction to a tarantula in Dr. No that climbed up his legs (while he was in bed) then across his shoulder. 007. Licence to smash.
Kiss of the Tarantula: None of Susan's victims are killed directly by tarantula bites. Two have fear-induced heart attacks and three kill themselves in a panicked crush inside a parked car.
Mike Nelson: Luckily for her, all her victims happen to have paralyzing spider phobias!
Continuing on the Indiana Jones theme, Willie Scott from Indiana Jones and the Temple of Doom has no problem around snakes, but once she discovers she's walking through a room covered in insects and other related critters, she practically freaks out. And she needed to cross the room in order to save Indy and Shorty from a Descending Ceiling. After much complaining, she does.
Zen from Chocolate goes into a screaming panic when exposed to flies. She's autistic, so she can't actually repress that reaction. It causes a lot of trouble for her when one of her targets turns out to be a butcher with extremely poor sanitation.
Groucho Marx as Captain Spaulding in Animal Crackers. After bragging about how brave he is, another character points out a caterpillar on his jacket and he immediately faints. The next Marx film, Monkey Business, has him brag that he's "whipped his weight in wild caterpillars", however, so this trait didn't carry between "characters".
Mice and Rats (musophobia)
The Chronicles of Narnia star Anna Popplewell (Susan) was so afraid of mice that the scene where the mice chew through the ropes binding Aslan's dead body had to be filmed in two separate places; one with poor Anna and one with the mice.
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. (Indy 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.) Must be a family thing (see also Indy's son being afraid of scorpions, above).
It makes sense. Indy's dad is a professor of Medieval studies and the bubonic plague which ravaged Europe in The Middle Ages was caused by fleas on rats.
Ace Ventura, as revealed in the second movie, when the sacred animal of the Wachatis turns out to be one.
When Alfred asks Bruce Wayne why he uses the bat as his symbol in Batman Begins, Bruce responds, "Bats frighten me. It's time my enemies shared my dread." This fear is also present in his initiation into the League of Shadows, his first encounter with the Scarecrow, and when he first finds the cave and is surrounded by swarming bats.
Interestingly, in Batman Forever he specifically says that a vision of bats only scared him at first.
In the same movie, The Riddler reacts with absolute terror after being beaten by Batman, going so far as to envision him as the same bat that young Bruce saw flying toward him as a child (a result of having used The Box to map Bruce's mind and learn his Secret Identity).
In some versions, Scarecrow himself has a fear of bats owing to his encounters with Batman.
Yuki from the first Ju-on has a huge phobia of cats, and is unable to even look at her friend Kanna's collection of cat ornaments and toys. Naturally, Toshio'sghostly cat companion, Mar, uses this to his advantage.
Subverted in Matilda. Ms. Trunchbull freaks out when she sees a black cat- and eventually kicks it. Matilda asks Ms. Honey if Ms. Trunchbull is afraid of cats. Ms. Honey replies "Black cats- she's very superstitious".
In The Black Cat with Bela Lugosi and Boris Karloff, Lugosi's character reacts violently to the sight of a cat. His fear only serves a purpose in one scene in the middle of the film. Mostly it makes the character even more unlikeable, as if Lugosi needed the help.
Frogs & Toads (batrachophobia)
Big Bully Troy from Max Keeble's Big Move is terrified of a giant Barney-like Scottish frog named McGoogles. That's, like, four fears in one.
In Star Trek, Bones reveals that he suffers from a "fear of dying in something that flies!"
Bones: Don't pander to me, kid, one tiny crack in the hull and our blood boils in 13 seconds. A solar flare might crop up and cook us in our seats. And wait till you're sittin' pretty with a case of Andorian shingles. See if you're so relaxed when your eyeballs are bleeding. Space is disease and danger wrapped in darkness and silence.
Kirk: Well, I hate to break it to you, but Starfleet operates in space.
In Freddy vs. Jason, Freddy is frustrated by finding out that Jason is invulnerable even in his subconscious, until he finds Jason's one buried fear: water. Considering that Jason's initial death as a little kid, which sparked off his entire series, was by drowning in Crystal Lake...yeah.
One of the Mogwai rules in Gremlins: Never get them wet.
In Gremlins 2: The New Batch, Brain Gremlin dies in the same way as the Wicked Witch of the West does. He must be afraid of water, too. No, Gremlins love water for the same reason mogwai owners are told to keep them away from water. Thing was, Billy then fried them all by releasing the trapped Electric Gremlin into the water.
Chief Brody from Jaws is afraid of water. And a good deal of people after having seen the movie, for that matter.
Susie, the little daughter of the hero in the original version of Piranha. With very good reason, in this case. Although when the piranha attack the camp she's attending she swallows her fear to try and save two of the camp counselors - she manages to rescue one of them...
Truman Burbank, The Truman Show (although, to be fair, he was only afraid of the ocean). Possibly an intentionally-coached phobia to discourage him from deciding to head out and learn the truth about his life.
Freddy Krueger is sometimes shown to be afraid of fire (understandably, due to having been burned to death by vigilante parents), which leads to an immensely satisfying moment in the first film...
While in the remake they ignore this completely due to his entire domain being filled with fire.
Other nature related phobias
During filming of The Lord of the Rings, Sean Bean was terrified of taking a helicopter to a filming location in the mountains. Enough that he took what to most people would be the far scarier option of climbing the mountain in full costume.
Toni, the punk-loving sister of the protagonist of 1982 Alone in the Dark is revealed to be afraid of the dark. It is also hinted to be so strong that it forced her to go to a mental institution in the past.
In Australian horror film Primal, one of the protagonists is revealed to be claustrophobic early in the film, when her friends find a tunnel through a mountain to the other side, where they're headed to see some ancient cave paintings. She has to drive the long way around after she gets a panic attack from entering. Later, the tunnel becomes the only viable way to escape the monsters, as the car's wheels are destroyed and the monsters won't go near the tunnel.
Sid Phillips, the main villain of Toy Story, actually gained a fear of toys at the end of the film as a result of a particular cowboy doll coming to life right in front of him.
So he ties them to the front of his garbage truck in the third film.
Buddy in the first Air Bud is subtly but strongly implied to be fearful of newspapers and loud thumps (often making it a point to retrieve the newspapers and bury them in the former and barking loudly during a court room when the Judge used his mallet regarding the latter). Considering the fact that he was exposed to them frequently by his former, extremely abusive owner, his fear is perfectly justified.