Final answer:
The exclusionary rule, which prevents evidence obtained through illegal searches from being used in trial, was declared in the Supreme Court case Mapp v. Ohio.
Step-by-step explanation:
The Supreme Court case that established the exclusionary rule is Mapp v. Ohio, ruling that evidence obtained in violation of the Fourth Amendment, which protects against unreasonable searches and seizures, is inadmissible in state courts. This landmark decision was made in 1961 and ensured that evidence collected through illegal searches could not be used to prosecute someone in a state criminal trial. The exclusivity rule was initially established on a federal level in Weeks v. United States in 1914, and Mapp v. Ohio extended its application to state courts.