Conservative commentator Bill Kristol recently suggested the U.S. Supreme Court Justice Samuel Alito enter the Republican presidential race, which prompted Scott Bomboy, writing for the Constitution Daily blog, to write about the long history of Supreme Court justices getting active in electoral politics.
For example, John Jay, the nation's first chief justice, ran twice for the governorship of New York without resigning. Justice Arthur Goldberg resigned from the court to be appointed as President Lyndon Johnson's ambassador to the United Nations.
However, most of Bomboy's examples are from the 1800s. A Supreme Court justice is much less likely to run for political office in today's political environment.