Did you have any other relatives who did? In my family, 1 grandfather and 1 aunt had it, and then I got it. Lots of people have red hair in my family, just not the tight little curls.
My mom used to get, uhm, frustrated you could say when people asked her if I'd played Annie (I think she got tired of people asking), but I loved it. Good thing, too, because nobody ever stopped asking, and I'm in my mid-20s now.