Final answer:
The U.S. Supreme Court case that established indigent felony defendants' right to government-paid legal counsel is Gideon v. Wainwright (1963). This case overruled a previous decision and expanded the Sixth Amendment's right to counsel to include state felony defendants who could not afford an attorney, significantly impacting the criminal court system.
Step-by-step explanation:
The U.S. Supreme Court case that held indigent defendants charged with a felony are entitled to the services of a lawyer paid for by the government is Gideon v. Wainwright, 372 U.S. 335 (1963). In this case, Clarence Earl Gideon was charged with a felony for breaking into and entering a poolroom. When he appeared in court without a lawyer, he requested the court appoint one for him, but the request was denied based on Florida state law at the time which only provided counsel in capital cases. Gideon, representing himself, was convicted and sentenced. He then appealed to the Supreme Court, which unanimously ruled that the Sixth Amendment's right to counsel in criminal cases extends to felony defendants in state courts and that it was consistent with the Constitution to require state courts to appoint attorneys for defendants who could not afford one on their own. This overturned the prior Supreme Court decision in Betts v. Brady, which had allowed states to deny counsel to indigent defendants when prosecuted by a state.
The Gideon v. Wainwright decision led to significant changes in the criminal court system, establishing the constitutional right to have an attorney provided at the state's expense to all defendants accused of a felony and paving the way for the creation of public defender systems. Due to the far-reaching impact of this decision, the courts have since extended the ruling to any case in which an accused might face the loss of liberty, and have overturned convictions where defendants had incompetent or ineffective lawyers.