The rosary was given to save the world!
The following text is taken from an interview with Sister Lucia, (one of the Fatima visionaries), by Father Fuentes in December 26, 1957
"Look, Father, the Most Holy Virgin in these last times in which we live has given new efficacy in the recitation of the Holy Rosary. She has given this efficacy to such an extent that there is no problem, no matter how difficult it is, whether temporal or above all spiritual, in the personal life of each one of us, of our families, of the families in the world, or of the religious communities, or even of the life of peoples and nations that cannot be solved by the Rosary. There is no problem, I tell you, no matter how difficult it is, that we cannot solve by the prayer of the Holy Rosary. With the Holy Rosary, we will save ourselves."
Bishop Fulton J. Sheen:
"If you wish to convert anyone to the fullness of the knowledge of Our Lord and to His Mystical Body, then teach him the Rosary. One of two things will happen. Either he will stop saying the Rosary — or he will get the gift of faith."
By Bishop Fulton J. Sheen
From the earliest days, the Church asked its faithful to recite the one hundred and fifty Psalms of David. This custom still prevails among priests, who recite some of these Psalms every day.  However, it was not easy for anyone to memorize the one hundred and fifty Psalms. Then, too, before the invention of printing, it was difficult to procure a book of the Psalms. That is why certain important books like the Bible had to be chained like telephone books are today; otherwise people would have run off with them.
Incidentally, this gave rise to the stupid lie that the Church would not allow anyone to read the Bible, because it was chained. The fact is, it was chained just so people could read it. The telephone book is chained, too, but it s more consulted than any book in modern civilization!
The people who could not read one hundred and fifty Psalms wanted to do something to make up for it. Therefore, they substituted one hundred and fifty Hail Marys. They broke up these one hundred and fifty, in the manner of the Acathist,  into fifteen decades, or series of ten. Each part was to be said while meditating on a different aspect of the Life of Our Lord.
To keep the decades separate, each one of them began with the Our Father and ended with the Doxology of Praise to the Trinity.
St. Dominic, who died in 1221, received from the Blessed Mother the command to preach and to popularize this devotion for the good of souls, for conquest over evil, and for the prosperity of Holy Mother Church and thus gave us the Rosary in its present classical form.
The Black Death, which ravaged all Europe and wiped out one-third of its population, prompted the faithful to cry out to the Mother of Our Lord to protect them, at a time when the present moment and death were almost one. 
The Black Death has ended. But now the Red Death of Communism is sweeping the earth (circa 1950). I find it interesting that, when the Blessed Mother appeared at Fatima in 1917 because of the great decline in morals and the advent of godlessness, she asked that, after the "Glory be" we add "have mercy on all souls; save them from hell and lead us to heaven."
It is objected that there is much repetition in the Rosary because the Lord's Prayer and the Hail Mary are said so often; therefore some say it is monotonous.
That reminds me of a woman who came to see me one evening after instructions. She said, "I would never become a Catholic. You say the same words in the Rosary over and over again, and anyone who repeats the same words is never sincere. I would never believe anyone who repeated his words and neither would God."
I asked her who the man was with her. She said he was her fiancé. I asked: "Does he love you?" "Certainly, he does," "But how do you know?" "He told me." "What did he say?"
"He said 'I love you.'"
"When did he tell you last?"
"About an hour ago."
"Did he tell you before?"
"Yes, last night."
"What did he say?"
"I love you."
"But never before?"
"He tells me every night."
I said: "Do not believe him. He is repeating; he is not sincere."
The beautiful truth is that there is no repetition in, "I love you." Because there is a new moment of time, another point inn space, the words do not mean the same as they did at another time or space.
Love is never monotonous in the uniformity of its expression. The mind is infinitely variable in its language, but the heart is not. The heart of a man, in the face of the woman he loves, is too poor to translate the infinity of his affection into a different word. So the heart takes one expression, "I love you," and in saying it over and over again, it never repeats. It is the only real news in the universe. That is what we do when we say the Rosary, we are saying to God, the Trinity, to the Incarnate Saviour, to the Blessed Mother: "I love you, I love you, I love you."
Each time it means something different because, at each decade, our mind is moving to a new demonstration of the Saviour's love.
The Rosary is the best therapy for these distraught, unhappy, fearful, and frustrated souls, precisely because it involves the simultaneous use of three powers: the physical, the vocal, and the spiritual, and in that order.
The Rosary is the book of the blind, where souls see and there enact the greatest drama of love the world has ever known; it is the book of the simple, which initiates them into mysteries and knowledge more satisfying than the education of other men; it is the book of the aged, whose eyes close upon the shadow of this world, and open on the substance of the next. The power of the Rosary is beyond description."
If you wish to convert anyone to the fullness of the knowledge of Our Lord and to His Mystical Body, then teach him the Rosary. One of two things will happen. Either he will stop saying the Rosary — or he will get the gift of faith. 
Catholic World News, 12/21/01, "Saying The Rosary is Good for You."
"Temporal punishment — It is the constant teaching of the Church that the voluntary act of penitential works has always been part of true repentance. The Council of Trent (Sess. XIV, c.xi) reminds the faithful that God does not always remit the whole punishment due to sin together with the guilt. God requires satisfaction, and will punish sin, and this doctrine involves as its necessary consequence a belief that the sinner failing to do penance in this life may be punished in another world, and so not be cast off eternally from God." Catholic Encyclopedia, 1918.
Fr. Patrick Payton lead 'The Family Rosary Crusade.'
Supremi Apostolatus Officio,' 1884
Cf. Rosarium Virginis Mariae,' n. 3
Cf. 'Augustissimae Virginis Mariae,' ('On the Confraternity of the Holy Rosary,') Encyclical of Pope Leo XIII, promulgated on December 12, 1897.
Enchiridion n.48. An indulgence is the pardon granted by the Church for the debt of penance we owe for sins. A plenary indulgence is a full pardon for such penances. A partial indulgence remits some penance owing. To gain a plenary indulgence you must be free from all attachment to sin, even venial sin. You must go to confession, receive Holy Communion, and pray for the intentions of the Pope.
Ibid. Five decades at least must be recited continuously, with devout meditation on the appropriate mysteries, which are to be announced if said aloud.
An Akathist (or "Acathist") in the Byzantine Church is a hymn of thanksgiving or supplication used on special occasions. It has a standard form comprising 13 sections, each one made up of a Kontakion and an Ikos. There are many different Akathist prayers in use in the Eastern Church. The one most widely known, however, dates from the early 7th century AD and is known as 'The Akathist to the Most Holy Theotokos.'
A brief presentation on this prayer can be found in the article Acathistus from the Catholic Encyclopedia. The term "Akathist" means "not sitting" which refers to the fact that it is celebrated in a standing posture.
The Black Death (bubonic plague with pulmonary infection), originated in Eastern Asia, passed through India to Asia Minor, Arabia, Egypt, Northern Africa, and directly to Europe by the Black Sea. In Europe, the epidemic began in 1346 and spread throughout Christendom, ending in 1353 on the shores of the Black Sea. The entire period was preceded by peculiar natural phenomena, as floods, tidal waves, and abnormally damp weather. The loss of human life in Europe alone is said to have amounted to twenty-five million people. The disease usually began suddenly and death occurred within three days. Great self-sacrifice was shown by the clergy, especially by the Franciscans, who are said to have lost 100,000 friars and nuns through the epidemic. (source: Catholic Encyclopedia, 1918.)
Excerpt taken from "Roses and Prayers," in the book 'The World's First Love,' by Bishop Fulton J. Sheen, publisher McGraw-Hill Book Company, Inc., New York, 1952.
Archbishop Sheen Today! -- Praying the Rosary
By Barbara Kralis
© Catholic Online 2004
The medical and scientific communities have recently proclaimed what Catholics have known for centuries — reciting the Rosary is good for you. 
However, the medical experts missed the raison d'être for the origin of the Rosary when they hypothesized it was developed by man to give those praying a sense of well-being as a result of their slowed cardiovascular rhythms.
Not quite, O men of modern science; but, nice try.
In truth, Heaven was the originator of the Rosary. The Blessed Virgin, in the 13th century, gave the Rosary to St. Dominic. Because belief of this Sacred Tradition requires faith, it is much easier to reason that man, for health reasons, devised the Rosary.
The above modern hypothesis is not entirely in the wrong, for there are a great number of benefits (graces) received by reciting the Rosary, both of the body and of the soul.
Praying the Rosary does bring us peace when prayed well and it consequently does slow down the cardiovascular rhythms of our body. More importantly, it gives us a more perfect knowledge of Christ. How does it do this?
The Rosary is 'a Christocentric prayer. It has all the depth of the Gospel message in its entirety.
The Rosary is the perfect compliment to the Holy Sacrifice of the Mass. It sustains and echoes our sacramental life. The Rosary is a 'path to contemplation' — a path that Pope John Paul II said he follows daily, realizing each day's work within the mysteries of the Rosary.
Moreover, the Rosary purifies our souls, gives us victory over our enemies, allows us to practice virtue, sends us graces and merits, and allows us to help pay our debts against our temporal punishment. 
The Rosary is also a prayer for peace in our families and in our world. What better time than in this era to pray the family Rosary, as Fr. Patrick Peyton instructed. He said, "The family that prays together, stays together." 
Pope Leo XIII, often called "the Pope of the Rosary," strived to maintain the tradition of this prayer, which he asserted was a strong spiritual weapon against evil. 
In addition, Sacred Tradition tells that The Fifteen Promises of the Virgin Mary (to those who recite the Rosary) was revealed in a message to St. Dominic and Blessed Alan 1208 A.D.
Our world owes a great debt of gratitude, perhaps more than our human minds can understand, to the holy St. Dominic. It is impossible to talk about the Rosary without significant mention of St. Dominic. Sacred Tradition and thirteen recent Popes tell us that Mary first revealed the Rosary devotion to St. Dominic.
Having received a vision of the Blessed Mother, Dominic began to spread the prayer of the Rosary in his missionary work among the Albigensians, a neo-Manichaean group of fanatical heretics. Albigenses believed that everything material was evil and everything spiritual was good. St. Dominic used the Rosary to convert the heretical Albigensians.
The Rosary was most strongly supported by the tradition of the Dominican Order. Pope Leo XIII affirmed over and over the Dominican origin of the Rosary and in a letter to the Bishop of Carcassone (1889), he accepts the tradition of Prouille, France, as the place where the Blessed Virgin Mary appeared to St. Dominic, revealing the devotion to the Rosary.
Pope Alexander VI in 1495, addressed St. Dominic as "the renowned preacher long ago of the Confraternity of the Rosary, and through his merits, the whole world was preserved from universal ruin."
During an interview that Pope John Paul II gave in Germany during 1980 he held up his Rosary and said:
"This is the remedy that should be used in the struggle against evil. Pray the Rosary daily."
Mindful of the action of Pope Pius V in the Battle of Lepanto, Pope John Paul II, said in his Angelus address of October 1983:
"It is not a question now of asking for great victories, as at Lepanto and Vienna, rather it is a question of asking Mary to provide us with valorous fighters against the spirit of error and evil, with the arms of the Gospel, that is, the Cross and God's Word. The Rosary prayer is man's prayer for man."
On 16 October, 2002 the Pope John Paul II began the twenty-fifth year of his service as Successor of Peter. He chose to celebrate his anniversary — the fifth longest Pontificate in history — by writing an Apostolic Letter: Rosarium Virginis Mariae, The Rosary of the Virgin Mary.
In one of the most beautiful of his documents Pope John Paul announces the Year of the Rosary — October 2002 — October 2003. He urges us to rediscover the Rosary: to 'contemplate with Mary the face of Christ.' 
Those who pray the Rosary regularly would do well to be enrolled in the Dominican Archconfraternity's Spiritual Rosary Confraternity.
As Pope Leo XIII said in his encyclical on the Confraternity, "whenever a person fulfills his obligation of reciting the Rosary according to the rule of the Confraternity, he includes in his intentions all its members, and they in turn render him the same service many times over." 
A plenary indulgence is granted if the Rosary is recited in a church, or public oratory or in a family group, a religious community or pious association; a partial indulgence  is granted in other circumstances." 
Carry your Rosary upon your person whenever possible. The popular devotion is the most powerful prayer outside of the Holy Mass. Do not miss one day without it.