H.D.
OH MY. You will get a lot of answers with this one! I have kids from 26 down to 5 and through the years the amounts have changed. First of all, what can you afford? If the going rate for allowance for a child her age is $20 a week that may be too much for your budget or be just right. In my opinion (I have a 13 year old) a child that age will do fine with $10 a week. No, it isn't enough to go to the movies every weekend, it shouldn't be! If you just give it to them enough to do whatever they want they won't know how to save for it. The adult world definitely doesn't work that way, right?
I always tell my kids, put 1/3 away for something big, 1/3 away for something small and the last spend now. It has worked for me, and them. Good luck!