Chisholm v. Georgia was one of the very first significant Supreme Court decisions. The details aren't that exciting, but the decision had a major impact on the development of the U.S. and the relationship between federal and state law. The first amendment added to the Constitution after the Bill of Rights was passed by the states due to this decision.
Alexander Chisholm sued Georgia for money owed by the state for Revolutionary War supplies delivered by Robert Farquhar (Chisholm was the executor of Farquhar's estate). The state declined to even respond to the lawsuit, claiming that as a sovereign state (an autonomous political entity) it couldn't be sued by an individual citizen. The Court ruled that the Constitution assigned the power to determine disputes between citizens and states to federal courts.
It only took one year for the states to overrule the decision with the 11th Amendment, which states, in full, "The Judicial power of the United States shall not be construed to extend to any suit in law or equity, commenced or prosecuted against one of the United States by Citizens of another State, or by Citizens or Subjects of any Foreign State." The concept of "11th Amendment immunity" has since become a major cornerstone of U.S. law, coming into play when individuals have legal disagreements with a state government.