In The Giver, what are the top government rules?

The main rule is that you never do anything to make anyone uncomfortable.

The community has many rules.  There is a rule governing almost all aspects of behavior.  All of the major rules have to do with making people conform.  This is known as Sameness.  Jonas describes the administration  of rules when his mother talks about her job in the Department of Justice.

Today a repeat offender had been brought before her, someone who had broken the rules before. Someone who she hoped had been adequately and fairly punished, and who had been restored to his place: to his job, his home, his family unit. (Ch. 1)

While it does not say what rules the man broke, he is in danger of being released if he breaks a third.  That means death by lethal injection.  Jonas and his mother do not know this, because no one in the community knows what release really means.

The community also has strict rules about how many children a family can have.  They can only have one boy and one girl.  The children are given to them by the community.  Teens are not allowed to go through puberty.  All teens and adults take pills for Stirrings, or hormones.

Stirrings. He had heard the word before. He remembered that there was a reference to the Stirrings in the Book of Rules, though he didn't remember what it said. And now and then the Speaker mentioned it. (Ch. 5)

The Stirrings pills rule is probably one of the most important ones in the community, because it prevents people from developing strong feelings.  The pills keep everyone under control.  They help keep the community free of emotions. 

The community's goal with Sameness is to make sure that everyone is completely calm.  Anything that might upset someone, whether language or actions, is not allowed.  This is why they kill one of the twins when identical twins are born.  Sameness is preferred, but identical is confusing and uncomfortable.