My parents didn't let us watch really scary movies but I do remember being afraid of ET (especially when he turned white, yuck!) and Gremlins! lol
I think my biggest fears developed after we moved from California to Missouri when I was 5. When we got to Missouri, my parents told us about a poisonous spider called the brown recluse that were in the area (and that we didn't have in CA), and even though you can recognize a brown recluse by the markings on their back, I was suddenly scared of all brown spiders thinking they were poisonous, and that soon transfered to just being scared of all spiders! And I am still afraid of spiders!
Likewise, when we got to Missouri my parents told us about tornados so we would be prepared in a tornado warning. Well of course I started being scared during every thunderstorm, thinking it would turn into a tornado, even though we only had tornado warnings and took shelter in the basement about once a year. Sadly that fear did eventually come true -- when I was in college a tornado went through our small hometown and destroyed nearly half of it, including most of the businesses and many homes (fortunately my house survived, and only a few people in town died, no one I knew). I still cry when I see pictures of all the devastation it caused. Now I'm extra scared of thunderstorms, especially since we do get tornados up here where I'm at grad school. (And on a side note, the devastation caused by Katrina reminds me so much of what my hometown looked like after the tornado, minus the flooding, and I really feel for those people since I've had a small taste of what they went through!)