As part of the U.S. Constitution's system of checks and balances, the powers of the Supreme Court of the United States are balanced by corresponding auditing authority of the other two branches of government: the legislative and the executive.
The legislative branch, represented by Congress, may impeach and remove justices of the Supreme Court for bad behavior. It can further act to limit the power of the Supreme Court by increasing its size, allowing more justices to be appointed. Finally, Congress has the "power of the purse strings" and allocates funding to the judiciary.
The executive branch, represented by the President, has the exclusive authority to appoint justices to the Supreme Court, thereby limiting its power by influencing its complexion and makeup.
Finally, the court is unable to issue advisory rulings, in contrast to constitutional tribunals in other countries such as France. The U.S. Constitution limits the court to hearing "controversies" and "cases." In the early republic, when George Washington requested an advisory opinion from the court, John Jay famously refused, citing the court's constitutional limitations.