The correct answer is Gideon v. Wainwright, 372 U.S. 335 (1963).
In it, the Warren Court ruled that states are obliged under the Sixth Amendment of the U.S. Constitution to grant an attorney to defendants in criminal cases who are unable to afford one. Florida law at the time ordered the designation of free attorney to indigent defendants solely in capital cases.
This case extended to the states the right to counsel, which the federal government was already required to by the Fifth and Sixth Amendments.