Crown v. Zenger (1735) -- One of the earliest cases tried in the United States, back when we were still a British colony. It established the right of newspapers to criticize government officials.
Near v. Minnesota (1931) -- Here, the Supreme Court ruled that the government may not prevent the press from printing a story (also called "prior restraint").
New York Times v. Sullivan (1964) -- This decision involved Martin Luther King, Jr. and accusations of libel.
New York Times v. United States (1971) -- The case of the "Pentagon Papers," in which the New York Times published documents revealing that the U.S. government had lied to the American people about our actions during the Vietnam War.