Classroom prayer (within Europe and North America) is teacher-led, predominately Judeo-Christian, state-sanctioned prayer in schools. The Supreme Court case Engel v. Vitale (1962) banned classroom prayer from public schools in the United States, and in Florida in 2009 school administrators were prosecuted for praying at a school-affiliated, adult-only event. Classroom prayer has been banned in government schools in most other Western European countries also.
Most private schools, even religious schools, imitate government and do not allow classroom prayer. Some Christian institutions, including many Catholic schools, do allow teacher-led prayers at special school events, such as school assemblies, school sporting events, and graduation exercises, but rarely allow it in the classroom. Some language teachers at religious schools teach the students the Lord's Prayer or the Hail Mary in the respective language(s) and begin each day's instruction with one or the other.
Christian homeschooling classes, in contrast, often begin with a classroom prayer.
Some private or religious schools hold religious assemblies, including religious services such as the Roman Catholic Mass, that permit prayer outside of the classroom, away from intellectual pursuits.
Prayer was encouraged, allowed and practiced in U.S. public schools from colonial times until 1962, when the U.S. Supreme Court in Engel v. Vitale banned school-led prayer, citing the First Amendment's prohibition on the government respecting an establishment of religion a precedent for its ruling. The UK has a little-observed legal requirement that all pupils "shall on each school day take part in an act of collective worship," except where the parent of the pupil has asked for the pupil to be excused from this.
Atheistic groups herald this as a great victory for their ideology, as since 1962 U.S. taxpayers have been compelled to fund and support a nominally secular but effectively atheistic position for the 90% of American students who attend public school. Supporters of the decision claim that there is a "separation of church and state" in the U.S. Constitution, echoing the phrase used by Jefferson in his letter to the Danbury Baptists, though no such phrase exists in the actual text of the First Amendment (the relevant part of the Constitution).
It has been demonstrated that when classroom prayer is allowed, a corresponding drop in crime, teen pregnancy, drug use, and obesity occurs, further bolstering the argument to allow prayer in the classroom. 
Examples of wrongful suppression of student prayer
Since 1962, and primarily since the 1990s, many students across the U.S. who engaged in prayer have found themselves targeted by overzealous teachers and school administrators.
In 1994, at Waring Elementary School in St. Louis, Missouri, fourth-grader Raymond Raines was sent to the principal's office after a teacher spotted him bowing his head in prayer before lunch. Raymond was eventually separated from his classmates and given a week's detention for his continued prayers. His mother, Ellen Raines, eventually withdrew Raymond from the school and enrolled him in a private school where he could practice his faith without persecution.. The liberal New York Times editorial page admitted that punishing a child for silent prayer would violate the First Amendment's Free Exercise clause.
On May 5, 1995, U.S. district judge Samuel Kent issued a ruling against students uttering the name of Jesus during prayer at a high school graduation in Texas, stating, "And make no mistake, the court is going to have a United States marshal in attendance at the graduation. If any student offends this court, that student will be summarily arrested and will face up to six months incarceration in the Galveston County Jail for contempt of court. Anyone who thinks I'm kidding about this better think again. Anyone who violates these orders, no kidding, is going to wish that he or she had died as a child when this court gets through with it."
On January 15, 2002, in Wilton, New York, kindergartener Kayla Broadus was stopped by her teacher from saying the "God is great, God is good" table prayer out loud with her friends before snack time. The Saratoga Springs City school district sided with the teacher, claiming the prayer was a violation of the supposedly constitutional "separation of church and state." Kayla's parents filed a lawsuit against the school and received a temporary restraining order from U.S. District Judge David Hurd on February 5, 2002, against the school's suppression of Kayla's prayer. On February 8, 2002, Judge Hurd issued a preliminary injunction against the school ordering it to allow Kayla to say grace with her friends. Following the injunction, the school decided to settle the embarrassing case, saying that Kayla could pray without inviting her friends to join her (as this was inexplicably deemed "disruptive").
From 2004 to 2006, a public school banned Bible study by children ... during recess. A teacher complained about the use of the Bible and the principal then censored the study activity, according to a sworn statement by a teacher told to stop it. Principal "Summa, having learned of a complaint by a teacher and of the students' Bible study, told fourth-grade teacher Virginia Larue to nix the group's recess meeting. Larue did, according to her deposition. In that sworn statement, Larue said she briefly informed Summa of a parental complaint about the Bible study, and Summa then instructed her to end the practice, citing fear over 'separation of church and state.' Larue later told one of Luke's Bible study colleagues the group could no longer meet at recess, according to the deposition."
In 2005, a New Jersey award-winning high school football coach, Marcus Borden, was ordered by his intolerant school district not to bow his head or "take a knee" during any player-initiated prayers. Borden resigned from coaching in October over the issue. Borden later sued and a trial judge ruled in his favor, but school officials and their allies appealed to the 3rd U.S. Circuit Court of Appeals. In a unanimous judgement from 2008, the court overturned the ruling of the trial judge, determining that Borden's actions would be construed by a neutral observer as promoting religion. In response, the superintendent of schools was "very pleased" with the ruling.
Classroom Prayer in Britain
See also Education in the United Kingdom
Many UK state schools, particularly Primary (Elementary) schools are Christian schools and have daily prayers and hymns at the beginning of the day, although atheists typically object to and prevent classroom prayer in UK schools just as in the United States. Over 1 million children in Britain attend schools connected with the Church of England. Such schools are funded by the government but attached to churches and as such, the children attend a religious service at least once a week during school time for a service where they pray together and receive blessings. Church schools are recognised for their distinctive Christian ethos and the impact this has on standards and all round education. The proportions of Church schools regarded as 'outstanding' (by Ofsted, the independent schools regulator) is much higher than the national norm and yet the Church schools are fully inclusive. 
- http://www.baptistmessenger.com/story/30D869A1C3EB8104A87DD4CA8659031D . They were ultimately acquitted.
- School Standards and Framework Act 1998 part 2 chapter 6
- Halverson, Delia T. Teaching Prayer in the Classroom: Experiences for Children and Youth. Nashville: Abingdon Press, 1989. Print.
- "Personal Prayer Is Not Illegal" New York Times Dec. 10, 1994