This is definitely more common then people think.
In my experience it's been more males then females (but that's my experience) with shots (clinics/hosptal/doctors office). The fear is expected with children but I work with adults. I have met adults that would do anything to not have a shot. When the fear is there it's overwhemling for the person.
The "art" of presenting with shots to patients is aquired (covering the tray, not preparing it in front of them etc...), the art of distractibility.
The dentist is a whole different monster (literally). Ahhhhhh
I do feel for the phlebotomist as that would almost be impossible to do with someone that has a phobia about needles.
I know many people think that the people are just chickens; so I thought I would take a stab at pointing out an explantion of support (or at least giving it a shot anyway).