The terms of Supreme Court justices are not specified, which means they can serve until they retire. The Constitution states that justices serve during good behavior, but they may be removed through impeachment.
It is extremely rare that a justice is impeached, and, in fact, this has only happened once as of 2014. Associate Justice Samuel Chase had articles of impeachment passed against him by the House of Representatives in 1805. The impeachment was spearheaded by President Thomas Jefferson, who thought the judiciary was seizing too much power. Justice Chase denounced the president's attempts to rid the courts of judges who had lifetime appointments. Judge Chase was eventually acquitted by the Senate. All other justices have served until death or retirement.