Is it normal for a grown man to be afraid of spiders?

Ever since I was a child I have had this fear of spiders. I can't go near them! As a boy I screamed the place down because one was crawling along the room, and even as an adult I caught a big spider actually crawing on me in the bathroom, I freaked, frightening my family in the process! They always seem to be crawling towards me and when I spot them they stop dead as if they know I have seen it. I can't kill them, I won't go near them. It's not just spiders, I also have a fear of being completly alone when the family are not there.