I used to be afraid of falling off.. but not anymore, assuming that it's just off to the side. A well-known rider (went to Royals and her mom also boards at my barn) from around here was killed when her horse accidentally ran over her after a jump, so that's always in the back of her mind. Although, I've always gotten up laughing whenever I've fallen.. except the one time where Major snuck in a buck and a quick pop to the side during a really relaxed canter at a show, I couldn't believe it!
I get nervous when I'm bringing Indie in or out and there's another mare by the gate since I'm worried that they'll just run right through me... even though they usually move once I hit them with the lead rope once or twice.
Right now, my one, unrational fear is of Indie getting hurt, becoming lame.. her arthritis being worse than the x-ray showed. (the x-ray just showed starting signs) Horses will be horses so I always remind myself of that.