While it's true that many judges on lower courts (state, appellate, and local courts) are elected by popular vote, just like any politician, the nine justices that serve on the United States Supreme Court are not. When the Supreme Court has a vacancy, the president nominates a replacement, who is then confirmed by the Senate.
How are justices to the U.S. Supreme Court elected? Is this a good or a bad thing?
Typically, presidents nominate persons for the Supreme Court who share their political and ideological views. Following a series of interviews, the Senate votes — if a majority of senators finds the candidate suitable, he or she is accepted onto the Court. If they do not, the president must nominate another individual. In recent years, Senate testimony has attracted more attention because more and more special-interest groups are lobbying senators to confirm or reject each nominee, depending on how each nominee's lifetime achievements and politics match with each group's interests and ideals.
Senate testimony is often just a formality, but the Senate periodically rejects a nominee. Two of President Reagan's nominees were rejected: Robert Bork, for his controversial opinions and his role in President Nixon's Watergate scandal; and Douglas Ginsburg, for his confession that he smoked marijuana with students while he was a professor.
Although Supreme Court justices serve a lifetime appointment (until death or voluntary retirement), the U.S. Constitution does allow for the impeachment of a Supreme Court justice. No laws detail what specifically constitutes an impeachable act, but it must be because of criminal or unethical acts rather than political disagreements. Justice Samuel Chase is the only justice to face impeachment. The House of Representatives impeached him in 1805, but Chase wasn't removed from the Court because the Senate's hearings revealed that Chase was impeached not because he had done anything wrong, but because his political enemies in the House disagreed with his decisions.
As to whether it's a good system or not, I'll leave that decision to you. Typically, because of their lifetime tenure, each president only replaces one or two Supreme Court justices (some presidents don't get to nominate anyone to the Supreme Court). This tends to keep the Court fairly balanced between conservative and liberal judges. What do you think of the system? Can you think of a better alternative?