The US Supreme Court had approximately 376 cases on its docket in 1963. Of those, the justices heard arguments in 131 arguments; dismissed 81 cases (most for lack of substantial federal question, some because they'd become moot); and disposed of 164 cases in other ways (mostly by vacating and remanding in light of whatever precedent(s) they believed applied - in 1963, the Supreme Court remanded many cases for a new trial due to their decision in Gideon v. Wainwright).
For more information, see Related Questions, below.
The US Supreme Court disposed of 197 published cases and motions during the 1972-1973 Term. Of these, they heard arguments in 153 cases. Five cases were considered under original jurisdiction (disputes between the states).
7,849 in a slow term
You can read all opinions from the 2008 Term on the Supreme Court website, via the Related Link, below.
The answer to this question would vary from Term to Term.
You can read all opinions from the 2006 Term on the Supreme Court website, via the Related Link, below.
The US Supreme Court had 73 cases scheduled for oral argument in the 2007-2008 Term; however, they only heard 70 and dismissed three without argument.
Judicial Review
Term
The Supreme Court is currently sitting for the 2009-2010 Term and has placed 85 merit cases on the calendar for argument. Five were dismissed prior to being heard, and one is scheduled for reargument, making the actual number heard 81. The Court disposed of a total of 92 cases in the 2009 Term. In the 2008-2009 Term, the Court wrote full opinions on 83 cases. For more information, see Related Questions and Related Links, below.
US Supreme Court statistics are reported by Term (first Monday in October to the following first Monday in October), not by calendar year. According to the most recent report, the Court reviewed 87 cases in the 2009-2010 term. This was approximately 1% of the total filed.
If you mean the collection of cases that the court will hear during a session or term, it is called the "docket", and this is the traditional word for that.
in the US Supreme Court, life
The US Supreme Court issued:87 Opinions in the 2005-2006 Term75 Opinions in the 2006-2007 Term73 Opinions in the 2007-2008 Term83 Opinions in the 2008-2009 TermThese numbers do not include In Chamber Opinions and other motions, but do include Per Curiam decisions.