While I've wondered if some of this is innate, I've come to the conclusion that much of it is either learned (often from parents) or experiential. There is certainly room here for a great "Nature vs. Nurture" debate, though!
In my own case, I have a phobia about flying, buzzing insects. While it's entirely possible that I learned this from my mother, who also dislikes bees and wasps, she has told me a story that would also explain my intense fear and strong reaction. Apparently when I was quite young, I was playing hide and seek and I hid next to a wasp nest, resulting in a very painful sting right above my eye. That would certainly have done it!
The strangest phobia I've heard was an older adult woman who was extremely afraid of chickens. I was much younger when I learned of her fear and I questioned her about it, curious to understand. She related that when she was a toddler, her family would visit her grandparents' farm...and they raised chickens. The roosters would attack her, hence her fear, which still remained many, many years later. Very logical, when explained in those terms.
About 5 or 10 years later, when we raised chickens for a couple years, I got to experience the behavior of a couple testosterone-driven roosters myself. Talk about aggressive! A full size rooster attacking a toddler would be very frightening and could inflict some painful damage. No wonder the little tyke was scared! The roosters were somewhat intimidating, even to big, old, adult-sized me.
I'm not sure what the statistics are, but I would guess that snakes, spiders, and bees/wasps are close to a 3-way tie for first place in the "feared animal" slot. Other animal phobias I've heard about include bats, cattle, dogs, and horses.
So what to do about it? The best suggestion I've got is to learn as much as you can about your fear. Talk to your parents, if possible, and see if they know why you are scared of that animal. Learn as much as you can about the animal, or class of animals. Finally, try to steel yourself to watch your problem animal going about its daily life. You will probably never be completely comfortable around one, but if you can stop the automatic runaway panic mode, you'll be both less embarassed and less likely to inadvertently pass along your fear to the next generation.
Have I taken my own advice? Yep. I can now photograph bees and wasps without even quaking inside, and I tend to freeze rather than run away, wildly swatting, if one unexpectedly buzzes me. I've actually taught myself to rescue a wasp caught in the house by putting an empty jar over it, sliding a stiff piece of paper over the jar mouth to confine the wasp inside, and then releasing the wasp back outdoors. (It seems like a much better solution than breaking out the pane of glass by hitting the wasp with a shoe, like I did in my 4th floor, college dorm room "a few" years ago!)
The best part of all is that, as you learn, you'll realize that spiders, snakes, and many bees & wasps are great predators who are working to help keep problem insects and rodents out of your yard and away from your home. Good luck! (And I'd be quite curious to hear your favorite phobia stories too.)