How many US Court of Appeals Circuit Courts are there?

Thirteen.

The US Courts of Appeals Circuit Courts are the thirteen intermediate appellate courts immediately below the US Supreme Court. Twelve of the Circuit Courts hear cases on appeal from US District Courts (trial) within their territorial jurisdiction; the thirteenth court, the US Court of Appeals for the Federal Circuit, has national subject-matter jurisdiction over cases initially held in the US Court of Claims, as well as appeals of patent, copyright, and a few other classes of cases.

Each Supreme Court justice has responsibility for handling emergency petitions for one or more of the Circuit Courts, which is a remnant of the "circuit riding" tradition, in which the Supreme Court justices traveled the circuits throughout the year, hearing cases in local forums.

1. US Court of Appeals for the First Circuit
2. US Court of Appeals for the Second Circuit
3. US Court of Appeals for the Third Circuit
4. US Court of Appeals for the Fourth Circuit
5. US Court of Appeals for the Fifth Circuit
6. US Court of Appeals for the Sixth Circuit
7. US Court of Appeals for the Seventh Circuit
8. US Court of Appeals for the Eighth Circuit
9. US Court of Appeals for the Ninth Circuit
10. US Court of Appeals for the Tenth Circuit
11. US Court of Appeals for the Eleventh Circuit
12. US Court of Appeals for the District of Columbia Circuit
13. US Court of Appeals for the Federal Circuit

For more information on the federal judiciary, see Related Questions, below.