The Supreme Court, known during it's time under the Galactic Empire as the Imperial Court, was the highest court of law in the Universe, during the time of the Old Republic. It was dissolved by Emperor Palpatine in 0 BBY, along with his dissolution of the Imperial Senate.
The Court consisted of twelve justices (each addressed as "Your Honor"); one of them was the Chief Justice who headed both the Court and the judicial branch. The Supreme Chancellor (and later the Emperor) nominated members of the Court.
The Supreme Court, in addition to serving as a 'court of last resort' and as a determiner of constitutional legality, also tried cases involving the most interstellar matters in the Republic (and some during the Empire), such as that of Supreme Chancellor Valorum, who they called before them over charges of corruption. However, at least some cases (including the trial of senators for treason) were handled by the Senate. The Court apparently had the ability to try the same case more than once; this may mean that the Republic's judicial system had no concept of double jeopardy. The Court had the ability to issue subpoenas and writs.