There are nine members of the Supreme Court, and that number has been unchanged since 1869. The number and length of the appointments are set by statute, and the U.S. Congress has the ability to change that number. In the past, changing that number was one of the tools that Congress used to rein in a president they didn't like.
Essentially, in the absence of legislated changes to the size and structure of the Supreme Court, appointments are made by the President as justices resign, retire, or pass away. Some presidents have nominated several justices: the first president George Washington nominated 11, Franklin D. Roosevelt nominated 9 over his four terms in office, and William Howard Taft nominated 6. Each of those was able to name a Chief Justice. Some presidents (William Henry Harrison, Zachary Taylor, Andrew Johnson, and Jimmy Carter), did not get an opportunity to make a single nomination.
Establishing the Supreme Court
The first judiciary act was passed in 1789 when the Supreme Court itself was set up, and it established six as the number of members. In the earliest court structure, the number of justices corresponded to the number of judicial circuits. The Judiciary Act of 1789 established three circuit courts for the new United States, and each circuit would be manned by two Supreme Court judges who would ride the circuit for part of the year, and be based in the then-capital of Philadelphia the rest of the time.
After Thomas Jefferson won the controversial election of 1800, the lame-duck Federalist Congress didn't want him to be able to select a new judicial appointment. They passed a new Judiciary Act reducing the court to five after the next vacancy. The following year, Congress repealed that Federalist bill and returned the number to six.
Over the next century and a half, as circuits were added without much discussion, so were Supreme Court members. In 1807, the number of circuit courts and justices was set at seven; in 1837, nine; and in 1863, the tenth circuit court was added for California and the number of both circuits and justices became ten.
Reconstruction and Establishment of Nine
In 1866, the Republican Congress passed an act reducing the Court's size from ten to seven in order to curtail President Johnson's ability to appoint justices. After Lincoln ended slavery and was assassinated, his successor Andrew Johnson nominated Henry Stanbery to succeed John Catron on the court. In his first year of office, Johnson implemented a plan of Reconstruction that gave the white South a free hand in regulating the transition from slavery to freedom and offered blacks no role in the politics of the south: Stanbery would have supported Johnson's implementation.
Congress didn't want Johnson to wreck the progress of civil rights that had been set in motion; and so instead of confirming or rejecting Stanbery, Congress enacted legislation that eliminated Catron's position, and called for the eventual reduction of the Supreme Court to seven members.
The Judiciary Act of 1869, when Republican U.S. Grant was in office, increased the number of justices from seven to nine, and it has remained there ever since. It also appointed a circuit court justice: the Supremes only had to ride circuit once over two years. The Judiciary Act of 1891 didn't change the number of justices, but it did create a court of appeals in each circuit, so the Supremes no longer had to leave Washington.
Franklin Roosevelt's Packing Plan
In 1937, President Franklin D. Roosevelt submitted a reorganization plan to Congress that would allow the Court to meet the problems of "insufficient personnel" and superannuated justices. In the "Packing Plan" as it was known by his opponents, Roosevelt suggested that there should be an additional justice appointed for every sitting one over the age of 70.
Roosevelt's suggestion arose from his frustration that his attempts at establishing a full New Deal program were being stymied by the Court. Even though Congress had a majority of Democrats at the time, the plan was resoundingly defeated in Congress (70 against, 20 for), because they said it "undermined the independence of the Court(s) in violation of the Constitution."
- Frankfurter, Felix. "The Business of the Supreme Court of the United States. A Study in the Federal Judicial System. Ii. From the Civil War to the Circuit Courts of Appeals Act." Harvard Law Review 39.1 (1925): 35-81. Print.
- Lawlor, John M. "Court Packing Revisited: A Proposal for Rationalizing the Timing of Appointments to the Supreme Court." University of Pennsylvania Law Review 134.4 (1986): 967-1000. Print.
- Robinson, Nick. "Structure Matters: The Impact of Court Structure on the Indian and U.S. Supreme Courts." The American Journal of Comparative Law 61.1 (2013): 173-208. Print.
- Schmidhauser, John R. "The Butler Amendment: An Analysis by a Non-Lawyer." American Bar Association Journal 43.8 (1957): 714-64. Print.