Yes they do. But the age of the child depends on the culture. Most Muslim families get their kid circumcised when they are about 1-2-3 years old. But in some cultures like Turks, they sometimes wait until the kid is 6-7-8 years old. So i guess the age limit is that getting him circumcised before he gets his teens.
I know my brother was about 7-8 years old when he was circumcised and i was 9 years old when i had mine.
Believe me its not a nice memory :) They put in about 5 needles and inject stuff in your personal area which should be a PERSONAL AREA!
They also celebrate the event as Jewish people do in Bar Mitzvah or the Latino people in Quinceanera. So many cultures see this event as a sign of stepping into manhood.