Galileo, though likely not the first person to use a telescope to observe the sky, did more than anyone to popularize the device and can be fairly called the father of modern astronomy. Galileo discovered the four largest satellites of Jupiter, and he was the first westerner to observe sunspots (there is an indication that chinese astronomers had already observed them).
His experimental work in dynamics paved the way for Isaac Newton's laws of motion, and he is often credited with being one of the first scientists to fully exploit the experimental method and to insist on a mathematical description of the laws of nature. His study of balls rolling down inclined planes convinced him that falling objects are accelerated independent of their mass, and that objects retain their velocity unless a force acts on them.
Galileo also described that a pendulum's swings always take the same amount of time, independent of the amplitude, a discovery which made later precise clocks possible.
Many of Galileo's theories exist today only in his notes and drawings. He created sketches of imaginary devices such as a candle and mirror combination to reflect light through an entire home, an automatic tomato picker, a pocket comb that doubled as an eating utensil, and what appeared to be a crude form of ballpoint pen.
A devout Catholic, his writings on the Copernican (incorporating a heliocentric, or sun-centered solar system) model of the universe disturbed the church. The Church, and most everyone else, held to a Ptolemaic, or Aristotelian view, incorporating an Earth-centered theory of the universe. Church fathers also argued extensively that any other view would contradict scripture. White  writes:
The war became more and more bitter. The Dominican Father Caccini preached a sermon from the text, "Ye men of Galilee, why stand ye gazing up into heaven?" and this wretched pun upon the great astronomer's name ushered in sharper weapons; for, before Caccini ended, he insisted that "geometry is of the devil," and that "mathematicians should be banished as the authors of all heresies." The Church authorities gave Caccini promotion.
Father Lorini proved that Galileo's doctrine was not only heretical but "atheistic," and besought the Inquisition to intervene. The Bishop of Fiesole screamed in rage against the Copernican system, publicly insulted Galileo, and denounced him to the Grand-Duke. The Archbishop of Pisa secretly sought to entrap Galileo and deliver him to the Inquisition at Rome. The Archbishop of Florence solenmnly condemned the new doctrines as unscriptural; and Paul V, while petting Galileo, and inviting him as the greatest astronomer of the world to visit Rome, was secretly moving the Archbishop of Pisa to pick up evidence against the astronomer.
But by far the most terrible champion who now appeared was Cardinal Bellarmin, one of the greatest theologians the world has known. He was earnest, sincere, and learned, but insisted on making science conform to Scripture. The weapons which men of Bellarmin's stamp used were purely theological. They held up before the world the dreadful consequences which must result to Christian theology were the heavenly bodies proved to revolve about the sun and not about the earth. Their most tremendous dogmatic engine was the statement that "his pretended discovery vitiates the whole Christian plan of salvation." Father Lecazre declared "it casts suspicion on the doctrine of the incarnation." Others declared, "It upsets the whole basis of theology. If the earth is a planet, and only one among several planets, it can not be that any such great things have been done specially for it as the Christian doctrine teaches. If there are other planets, since God makes nothing in vain, they must be inhabited; but how can their inhabitants be descended from Adam? How can they trace back their origin to Noah's ark? How can they have been redeemed by the Saviour?" Nor was this argument confined to the theologians of the Roman Church; Melanchthon, Protestant as he was, had already used it in his attacks on Copernicus and his school.
Despite his continued insistence that his work in the area was purely theoretical, despite his strict following of the church protocol for publication of works (which required prior examination by church censors and subsequent permission), and despite his close friendship with Maffeo Barberini who later became Pope Urban VIII and presided throughout the ordeal, Galileo was forced to recant his views repeatedly and was put under life-long house arrest (1633-1642).
On June 22 1633, the Roman Inquisition started its trial against Galilei, who was then 69 years old and pleaded for mercy, pointing to his "regrettable state of physical unwellness". Threatening him with torture, imprisonment and death on the stake, the show trial forced Galileo to "abjure, curse and detest" his work. Galileo did everything the church requested him to do. That the risk of torture and death Galileo was facing was a real one had been proven by the church in the earlier trial against Giordano Bruno, who was burned at the stake in 1600 for holding a naturalistic view of the universe.
Galileo was first imprisoned and put under house arrest shortly after, where he later went blind. Under arrest, he was forced to recite penitentiary psalms regularly. His Dialogue was put on the Index librorum prohibitorum, a black list of banned books, until 1822. 
Galileo is a classic case of a scholar forced to recant a scientific insight because it offended powerful, conservative forces in society: for the church at the time, it was not the scientific method that should be used to find truth -- especially in certain areas -- but the doctrine as interpreted and defined by church scholars, and this doctrine was defended with torture, murder, deprivation of freedom, and censorship.
In 1992, 359 years after the Galileo trial, Pope John Paul II issued an apology, lifting the edict of Inquisition against Galileo: "Galileo sensed in his scientific research the presence of the Creator who, stirring in the depths of his spirit, stimulated him, anticipating and assisting his intuitions."
-  Andrew Dickson White: A History of the Warfare of Science with Theology in Christendom. New York 1898. Public domain text, online version.
-  Hal Hellman: Great Feuds in Science. Ten of the Liveliest Disputes Ever. New York: Wiley, 1998.