Taylor Swift. She freaked out on the way to film a scene for the "Love Story," music video because there was a spider on her dress.
Like his best known character, Ron Weasley, Rupert Grint is terrified of spiders and claimed that he couldn't even watch the scenes with the giant spiders in the Chamber of Secrets.
Robert Fuller. His Emergency! castmates found lots of ways to playfully torment him with it.
Napoleon was scared of cats. Maybe if his enemies knew that, he would have been defeated after his first battle; the caricaturists that represented him riding a cat◊ (supposed to be his marshal Michel Ney, a.k.a the Red Lion) obviously didn't.
It wasn't without malice that the Cheshire Cat was made into a scapegoat in Tim Burton's 2010 version of Alice in Wonderland; Burton really hates cats. Whether this is a phobia or not depends on who you believe.
This is a fairly common phobia in India, Nigeria, and most countries where fewer people keep dogs as pets.
This might partly be caused by the fact that such countries frequently have a large number of stray and feral dogs roaming about.
Genghis Khan was afraid of dogs. (And you can't blame him; a lot of breeds of dogs in Mongolia tend to be mean.)
David Boreanaz has a phobia of chickens. It made the Bones episode "The Tough Man In The Tender Chicken" rather interesting behind the scenes
Bea Arthur also had a chicken fear. The Golden Girls scene where Rose brings home a live chicken had to be restaged to make things easier on Bea.
During the making of Aladdin when they brought in live parrots as reference for Iago, the crew learned that Jonathan Freeman, who voices Jafar, has a fear of birds.
Michael Strahan is afraid of snakes.
From Dusk Till Dawn star Salma Hayek has a real fear of snakes, and had always refused to be near them. When she read the script, she knew that her phobia would prevent her from taking the part of Satanico Pandemonium, but Robert Rodriguez conned her into thinking that Madonna was ready to take the part instead, so she spent two months with therapists in order to overcome this fear.
Rooster Teeth has Geoff Ramsey, a man who's covered in tattoos but is petrified by snakes.
Other animal phobias
Read anything from the Cthulhu Mythos and remember that HP Lovecraft was afraid of fish. (Possibly the fact that he had an anaphylactic allergy to shellfish had something to do with it.)
Kevin Smith is reportedly deathly afraid of sharks (galeophobia). Ironically, Jaws is one of his favorite movies.
General Andoche Junot apparently had an irrational fear of toads, to the point that he completely freaked out at the battle of Vimeiro because he had seen one on the road (that, or he was just drunk).
Special effects legend turned actor Tom Savini is terrified of cockroaches. When he was working on Creepshow, specifically the segment "They're Creeping Up on You", one of the cockroaches touched his ankle. Savini has no memory of actually crossing the room, but he ended up on the other side of it.
While "camel spiders" (which aren't spiders) are not actually very dangerous, there's a lot of misinformation out there about them, most of which makes them sound scarier than they are. Freaking out is predictable if you think something can literally gouge out chunks of your flesh.
David Attenborough hates rats, though he hides it well on-camera; one episode of his series The Life of Mammals shows him presenting in the middle of an Indian temple devoted to rats.
During interviews where Ghostbusters is the topic, Rick Moranis, known for his role as Louis Tully in the movies, claims to be afraid of ghosts.
"Yeah, ghosts. Scare the pants off me. The polyester pants off me."
Voice Actor J. Michael Tatum once told a story of him going to a halloween fun park. Two clowns followed him around the park and in the end he punched one of them, opting him to get kicked out of the park.
Flying (aviophobia) or Heights (acrophobia)
Filmmaker Lars von Trier rarely moves far from the border of his native Denmark, and has never left Europe due to an intense fear of flying. He even turned down an offer to direct for Steven Spielberg due to this.
Stanley Kubrick also had a fear of flying, and as a result, spent the last 40 years of his life in England.
Former soccer player and now sports coach Marcelo "Bichi" Borghi is also infamous by his fear of planes. The very few times he doesn't travel by bus/train/car with his teams, he has to be sedated to the point of almost passing out when on the plane.
Another soccer example, former Inter Milan and Arsenal striker Dennis Bergkamp; who refused to go to the 2002 World Cup (in South Korea and Japan), because it would require him to fly. He traveled by boat for international/European matches.
Legendary American Football announcer John Madden was famous for his aviophobia. This gave him his iconic trademark - the Madden Bus.
General of the Air Force Henry "Hap" Arnold was one of the first military aviators, and would eventually rise through the ranks to become the first (and only - the 5-star ranks were discontinued after World War II) General of the Air Force. He was also afraid of flying, due to being one of the first military aviators to be in a plane crash.
There was a reason Randolph Mantooth's character John Gage did more high altitude rescues on Emergency!. Kevin Tighe, who played Roy Desoto, is afraid of heights.
Tom Petty is also afraid of heights. In the video for "Free Fallin'", when he appears to be hovering over the opening scene wearing shades, he was strapped into a crane to achieve the effect. He wasn't wearing the shades to look cool, but to hide how terrified he was.
Hitchcock also had a lifelong fear of policemen (dating from a childhood Scare 'Em Straight incident), which is why so many of his protagonists end up wrongly accused.
Interestingly, this type of fear is acknowledged in an episode of Full House.
Joey: Some people are afraid of the dark. Some people are afraid of heights. Some people are afraid of eggs. Jesse: Eggs?
In a magazine from years ago, Hilary Duff stating her fear (or strong disgust) of eggs.
Stephen King is afraid of the number 13, a condition known as triskaidekaphobia.
Composer Arnold Schönberg similarly was afraid of the number. His greatest fear was reportedly dying on an age whose digits added up or multiplied to 13. Which he did, at age 76 (7+6=13) on Friday the 13th - perhaps because he feared it that much.
French composer Jules Massenet shared their fear as well. Made weirder and arguably funnier by how the letters in his name are... thirteen.
Pamela Anderson probably has the above beaten. She is reportedly a sufferer of eisoptrophobia — in other words, she is freaked out by her own reflection.