Answer:
General Information
The United States has many Courts of Appeal. Some are general jurisdiction courts; others deal with special subject matter such as Veterans' Claims or the Armed Forces. For the purpose of this question, we will talk only about the 13 Circuit Courts that are the primary source of cases reviewed by the US Supreme Court.
The US Court of Appeals Circuit Courts are the intermediate step in the judiciary process, above the District Courts (trial courts), but below the Supreme Court. Twelve of the Circuit Courts are responsible for cases heard in regional District Courts, while the thirteenth, the US Court of Appeals for the Federal Circuit, is a national court that considers appeals from a variety of limited subject courts that are too small to have a dedicated appellate court.
The number of judges on a Circuit Court varies according to the population density and case load of the territory for which it's responsible (more below). Each Circuit has one Chief Justice and a variable combination of active-status (full-time) and senior (semi-retired, part-time) judges.
Generally, appeals cases are heard by panels of three judges that are randomly selected from the pool of all available judges (including those on senior and temporary assignment status), but under certain circumstances cases may be heard en banc (by the full court of active-status judges). This may occur if a majority of active-status judges vote that they need to consider the verdict as a group, to ensure uniform decisions on similar cases, or if the question is exceptionally important. The Courts also have the discretion to consider a petition for an en banc hearing from one of the parties in the case, if they believe the party's reason is compelling.
Regardless of the panel size, decisions are made by a simple majority of votes.
US Court of Appeals Judges
First Circuit:
06 Number of Active Seats Allocated
01 Vacancies
03 Senior judges
09 Total Seats
Second Circuit:
13 Number of Active Seats Allocated
04 Vacancies
12 Senior judges
25 Total Seats
Third Circuit:
14 Number of Active Seats Allocated
02 Vacancies
09 Senior judges
23 Total Seats
Fourth Circuit:
15 Number of Active Seats Allocated
05 Vacancies
03 Senior judges
18 Total Seats
Fifth Circuit:
17 Number of Active Seats Allocated
01 Vacancies
06 Senior judges
23 Total Seats
Sixth Circuit:
16 Number of Active Seats Allocated
01 Vacancies
10 Senior judges (An additional 4 on inactive status)
26 Total Seats
Seventh Circuit:
11 Number of Active Seats Allocated
01 Vacancies
05 Senior judges
16 Total Seats
Eighth Circuit:
13 Number of Active Seats Allocated
00 Vacancies
09 Senior judges
22 Total Seats
Ninth Circuit:*
29 Number of Active Seats Allocated
02 Vacancies
19 Senior judges
48 Total Seats
Tenth Circuit:
12 Number of Active Seats Allocated
00 Vacancies
10 Senior judges
22 Total Seats
Eleventh Circuit:
12 Number of Active Seats Allocated
01 Vacancies
06 Senior judges
18 Total Seats
D.C. Circuit:
11 Number of Active Seats Allocated (was reduced by one seat in 2007)
02 Vacancies
05 Senior judges
16 Total Seats
Federal Circuit:
12 Number of Active Seats Allocated
00 Vacancies (one vacancy is expected in October 2009)
04 Senior judges
16 Total Seats
Totals
181 Active-status Seats
020 Current Vacancies
101 Senior-status Judges
282 Total Available on August 18, 2009**
** Bear in mind this number can fluctuate, as senior judges go into full retirement or die, and if temporary assignment judges are added. Temporary assignment judges may come from other Circuits, from retired judges and justices, and from District Courts. Vacancies are counted as Active-Status Seats, despite being unfilled.
* Due to the size of the 9th Circuit, this Circuit uses a limited en banc panel of 11 judges.