Also See Is School Prayer Actually Prohibited (below)
Prayer in schools prior to 1962 was utilized in school districts all over the U.S. in many varieties. Some teachers used extemporaneous prayers, simply expressing their thoughts and desires; others implemented structured prayers, such as the Lord's Prayer or the 23rd Psalm, or others approved by local school boards. New York students prayed each day:
"Almighty God, we acknowledge our dependence on Thee and beg Thy blessing over us, our parents, our teachers, and our nation."
It was this simple prayer which came under fire and went to the Supreme Court for the landmark decision.
Much has been said both for and against prayer in schools. There is little doubt that neither the Lord Jesus Himself nor the founding fathers would have been in favour of ‘forced’ or ‘state sponsored’ prayer. The option to pray or not to pray is a matter of individual choice and has to come from the heart. It is a matter of some doubt whether the actual doing away of prayer in schools has directly contributed to the escalation of teen-age pregnancies and suicides and the downward spiral of the SAT scores.
The Pharisees thought they would be heard for their ‘much speaking’, and similarly it is questionable as to how much value there is in a ‘canned’ prayer even if recited by thousands of young people across the country. (Consider that most schools in India start their day with a very generic prayer, similar to the one that sparked the U.S. Supreme court’s decision on the Engels v. Vitale case in 1962).
What Really Caused The Downward Spiral?
In the words of Greg Koukl..
Some have suggested that there is a causal relationship between taking prayer out of school and all the other bad things that happen in our society. I'm not sure that it's valid. The rooster crows and the sun comes up. Does that mean that the rooster causes the sun to come up? Because the sun comes up after the rooster crows, does it mean that if we killed the rooster we'll be perpetually in darkness? The point is that just because one thing happens after another doesn't mean that the second is caused by the first. 
However some indisputable statistics tell us that the downward slide in behavior started about the time of the court decision and was very evidently related. As we see it, the court ruling to remove prayer from the school system was nothing more than the ‘official’ stamp on the removal of God from a very crucial part of our society. It was simply one large step among many small ones, which has contributed to the moral & spiritual disintegration of the US. It was a flying leap across the narrow chasm separating a God fearing moral country and the chaotic ‘everything goes’ situation we find ourselves in today. The message the Supreme Court sent to the country that fateful day was that it was okay to ‘remove’ God from His rightful place. They were simply another, very effective, tool in Satan’s hand
Remove the fear of God from the human heart, whitewash the reality that, sooner or later, all of us will answer to a supremely moral Being, eliminate the concept that He demands adherence to His laws and it is but a short step to the deterioration of the cornerstone of society… The Family. With the fear of God done away with there is no longer any reason to treat the marriage vows as sacred, to bring up God-fearing children. From there it is an even shorter step to all the other sinister and evil circumstances we find ourselves in today…. Teen pregnancies, violent crime, suicide, drugs and alcohol abuse are the very logical fruits of a society that has forgotten that He is a God of wrath. See The Wrath of God
The elimination of the fear of God, symbolized by the Supreme courts actions in the matter of school prayer, led to a dramatic increase in crime, venereal disease, premarital sex, illiteracy, suicide, drug use, public corruption, and other social ills. See Should Christians Fear God?
Putting Prayer Back In Schools?
Putting prayer back into schools may do more harm than good... In the words of pastor Greg Koukl
…. It may be that the thing that has caused our decline was not pulling prayer out of schools, but there is a third thing that caused both the decline and the pulling of prayer out of schools. The reason that's important is that if we try to fix the problem by putting prayer back into schools, and taking it out wasn't the thing that caused the problem, then we are kind of fixing the wrong part of a machine that's not working. But in the process of fixing we could do more damage, and this is a big concern that I have. You have to be careful of making decisions based on what appears to be a causal relationship if there isn't in fact a causal relationship. ...
“now that it's gone you will not be able to get back in the schools what was lost because if we reintroduce prayer in schools in any sense it's going to be kind of a benign civil religious prayer that satisfies everyone and offends no one... I think it may end up doing more harm than good by teaching people that as long as you have a kind of a benign, broad-brushed reference to some kind of deity then you are doing okay, and the details don't really matter that much. That would be a terrible message to send to young people.” 
 Gregory Koukl. School Prayer: The Wrong Hill to Die On.