Final answer:
The Engel v. Vitale case ruled that official school prayers mandated by states for students to recite are unconstitutional, as they violate the Establishment Clause of the First Amendment. Subsequent cases have reinforced this decision, emphasizing the separation of church and state in public schools.
Step-by-step explanation:
The case that ruled it was illegal for states to require official school prayers to be recited by students is Engel v. Vitale. In Engel v. Vitale, the Supreme Court deemed that the recitation of a nondenominational prayer, even though it did not endorse any specific religion, was unconstitutional as it violated the Establishment Clause of the First Amendment. This landmark decision, alongside others such as West Virginia State Board of Education v. Barnette, Abington School District v. Schempp, and Santa Fe Independent School District v. Doe, cemented the principle that public school-led prayers are an unconstitutional endorsement of religion.
While prayer itself in schools is not illegal, the Establishment Clause prohibits government-led or endorsed religious practices, ensuring a separation between church and state and protecting individual religious freedoms.