Answer
The US Supreme Court currently exercises original jurisdiction over only one type of case: disputes between the States. Until 1978, cases against foreign ambassadors also began in the Supreme Court; however, Congress relieved the Court of exclusive jurisdiction when it amended the federal law (28 USC § 1251) to allow US District Courts to hear these cases first.
The Supreme Court may choose to try a case involving ambassadors or other foreign dignitaries, but is more likely to remand this class of case to US District Court.
Cases that MUST begin in the US Supreme Court:
public ministers, consuls, or vice consuls of foreign states are
parties
28 USC § 1251
(a) The Supreme Court shall have original and exclusive
jurisdiction of all controversies between two or more States.
(b) The Supreme Court shall have original but not exclusive
jurisdiction of:
(1) All actions or proceedings to which ambassadors, other
public ministers, consuls, or vice consuls of foreign states are
parties;
(2) All controversies between the United States and a State;
(3) All actions or proceedings by a State against the citizens
of another State or against aliens.
Public Law Amendment
1978 - Subsec. (a). Pub. L. 95-393, Sec. 8(b)(1), designated introductory provision of subsec. (a) and (a)(1) as (a), and struck out "(2) All actions or proceedings against ambassadors or other public ministers of foreign states or their domestics or domestic servants, not inconsistent with the law of nations". Subsec. (b)(1). Pub. L. 95-393, Sec. 8(b)(2), substituted "to which ambassadors, other public ministers, consuls, or" for "brought by ambassadors or other public ministers of foreign states or to which consuls or".
Amendment by Pub. L. 95-393 effective at the end of the ninety-day period beginning on Sept. 30, 1978, see section 9 of Pub. L.95-393, set out as an Effective Date note under section 254a of Title 22, Foreign Relations and Intercourse.
For more information, see Related Questions, below.
Supreme Court of the United States
The Justice Department tries cases of treason.
Section 2 of Article III of the constitution sates:"In all cases affecting ambassadors, other public ministers and consuls, and those in which a state shall be party, the Supreme Court shall have original jurisdiction."The Supreme Court has original jurisdiction in cases involving two states, and cases involving ambassadors, consuls, or other public ministers.This is not to be confused with appellate jurisdiction. Original jurisdiction is when the court hears the case first. Appellate jurisdiction is when the court hears an appeal from another court of original jurisdiction.
The Supreme Court of Canada is the highest judicial body in Canada. It hears final appeals and decides on issues that are relevant to all Canadians. The government may also ask for a reference from the Supreme Court if it needs advice on a particular issue.
The Supreme Court is the most powerful federal court. The Courts of Appeal are the most powerful courts most litigants will ever reach (the Supreme Court only hears a tiny number of cases a year). The District Courts are the trial level courts.
The Supreme Court hears cases which are on final appeal. The Supreme Court also hears cases relating to national elections.
The Supreme Court hears the most important cases.
The types of cases that Australia's high court hears are those cases which come to it on appeal and those cases which needed interpretation of the Constitution.
Supreme Court of the United States
The Supreme Court of Canada is the highest court in the country. It hears appeals fro the provincial Courts of Appeal
The Supreme Court hears the largest number of cases. They have the power to decide appeals on all cases from the other levels of court.
Federal appellate cases
The Supreme Court justices hear cases in the courtroom of the Supreme Court Building in Washington, DC.
The Supreme Court hears an average 75 cases in a year
The Supreme Court hears any cases that involve the interpretation of the Constitution.
Federal Appeals Courts
No. The Supreme Court can't demand an investigation for most of the cases it hears because 1) that isn't a judicial function; and 2) most cases arrive at the Supreme Court on appeal. Appellate courts are required to accept the facts of a case as presented; they don't order or consider new evidence.