Engel v. Vitale (1962)
In 1962 the Supreme Court decided the case of Engel v. Vitale challenging organized prayer in schools.  The case had been brought by parents of ten students at New Hyde Park High School in New York, who had to start school each day saying aloud the following prayer:  "Almighty God, we acknowledge our dependence upon Thee, and we beg Thy blessings upon us, our parents, our teachers and our Country."

They argued that the state law requiring this prayer was a violation of the Establishment clause of the First Amendment and the separation of Church and State because it furthered the religious beliefs of one particular group. 

A New York State Court had ruled in favor of prayer in schools as long as the schools did not compel students to join in over their or parental objections.  But the Supreme Court disagreed, and stated that prayer in public schools "breaches the constitutional wall of separation between Church and State...in this country, it is no part of the business of government to compose official prayers for any group of the American people to recite as a part of a religious program carried on by government."

1. Listen to the oral argument: http://www.oyez.org/oyez/resource/case/111/
2. Read the decision: http://caselaw.lp.findlaw.com/scripts/getcase.pl?court=US&vol=370&invol=421