I have a totally irrational fear - phobia, actually - of cats. I can't bear for a cat to come within ten feet of me.
Strangely enough, I have also just in the last few years developed a fear of heights, where it never used to bother me in the slightest. That puzzles me, as I thought phobias were things you either had throughout life, or were caused by a significant event. There has been no event in my life to suddenly cause me to be afraid of heights.