The BBC reported last year on Rwanda's efforts to limit family size. In the aftermath of the genocide in 1994, Rwanda has the highest birthrate in the world. See the article linked below.
It is not state regulated, but many people in India practice population control with "selective abortion." Because of the high cost of providing a dowry for their daughters when they get married and the need for sons to work, some families will abort their babies if an ultrasound shows they're having a girl. They are at the point now where there are not enough girls for Indian men to marry. See the article linked below.
The only country that I know of and I'm sure there are more is the People's Republic of China (PRC) which have a One Child Policy in place for rural and urban areas. It's enforced fairly strictly in most regions. People are also allowed to have two children in cases where the first born child is a girl, because girls cannot carry on the family lineage and are not deemed as valuable as boys, or if the first born child is disabled in such a way that it would not be optimal if that child were to reproduce some day.
The PRC's policy is one that is centered around controversy because it infringes on basic human rights, but the laws are enforced in an effort to control over population since it is a problem in the country and tends to drain resources.
This is a pretty good link that explains the policies in more detail:
In The Giverthe reasons were much the same. They wanted a Utopian society. The society had to be controlled on all levels, down to the memories in order to ensure absolute peace. People's experiences had to be equal and limited in order to keep everyone relatively happy.