According to the U.S. Constitution, states are not permitted to enter into a treaty, coin money, emit bills of credit, pass any bill of attainder or grant titles of nobility. There are numerous other restrictions on states posed by the U.S. Constitution, but these restrictions are also often met with exceptions based on particular circumstances.
As the Founders were constructing the Constitution, they utilized their knowledge of weaknesses and violations they witnessed in the British Parliament as well as their newfound beliefs in a republican government to determine these prohibitions to the states.
No state is permitted to enter into a treaty, alliance or confederation. The U.S. Constitution aimed to be the source of any control over foreign affairs, rather than delegating that power to the individual states. Since treaties, alliances and confederations are binding international agreements between nations, it was deemed necessary to prohibit states from being able to enter into them independently.
No state is permitted to coin money. The Constitution gave exclusive power over the coinage of money to the federal government.
States cannot emit bills of credit to the United States. This clause has evolved over time due to specific needs during war time in the United States.
The states are not permitted to pass bills of attainder. It was determined that bills of attainder were a violation to civil liberty and were banned to the states. This opinion by the Founders of the nation was fostered by their experience with British Parliament using bills of attainder to carry out punishments for treason, and they decided against allowing it in the United States.
Granting titles of nobility is not a power that is given to the states. This measure was passed in order to prevent diminishing or harming the republican character of the American government.