"The Volturi aren't supposed to be the villains, the way they seem to you. They are the foundation of our peace and civilization."
For the violation of any laws it is death, and more often than not, without trial.
Immortal children are not to be created, since they are notoriously incapable of self-control and therefore can lead to possible exposure of the vampire world.
This includes lying or giving any false information to the Volturi, again under pain of death, and regardless of intent to lie.
There is to be no hunting in Volterra, where the Volturi reside. The Volturi themselves do not hunt within the city walls, bringing their food in from the outside, sometimes quite far away. Vampires must hunt inconspicuously, choosing targets that are likely to be missed, disposing of the remains and often changing hunting territory.
Releasing newborn vampires without training and lack of control during that period is prohibited. There are methods to do so, though they often require more than one mature vampire.
No Rebellion Plotting
It is death without trial for anybody involved in an attempted plot to overthrow the Volturi (it is nearly impossible to succeed)
All vampire laws centre around the fact that vampires cannot be conspicuous to humans.