States must have a republican form of government. This is to ensure that no individual should gain too much power in one state.
States are given the power to create their own laws. They are also given the power to enforce those laws.
Each state must respect the laws of each individual state. This also extends into court decisions in which the states must respect those as well.
New states can only be admitted by both the president and congress. They must both be in agreement or else the state can not be legally admitted.
If a criminal tries to flee to another state, the state can request that the criminal be returned to face charges. This helps cut down on crimes in which the answer was simply to go to another state and get off free.