Galileo Galilei (1564-1642) is best known for his theories of celestial motion, which contradicted the view that the Earth was fixed in the heavens and all other heavenly bodies revolved around it. Basing his ideas about celestial motion on his actual observation of the planets and their moons through a telescope, Galileo realized that the ancient theories of Ptolemy (which placed the Earth at the center of the universe) were incompatible with his observations. Through these observations he was able to confirm many of the theories of Nicholas Copernicus who had made similar arguments, but lacked observed data.
In 1632 Galileo published his Dialogues on the Two Chief Systems of the World and immediately found himself in trouble with the Catholic Church. Summoned to Rome by the Inquisition on September 23 1632, he was put on trial and following the verdict of the Inquisition was forced to renounce his beliefs in Copernican theory and the motion of the earth. The original verdict condemned him to life in prison, but was amended the following day to house arrest, a sentence that remained in force until his death. His book (Dialogues) was banned by the Catholic Church and only in the 1990s did the Church recant its condemnation of Galileo.
For more background on the issues and the players, you can read Galileo's own exposition of his views about the relationship between science and religion in his Letter to the Grand Duchess Christina of Tuscany (1615); you can read what the Catholic Church had to say about Galileo as late as 1913 in an essay in the Catholic Encyclopedia or in an recent essay from the Vatican Observatory; or you can read more about Galileo himself. By far the most comprehensive site devoted to Galileo's life and work is the Galileo Project at Rice University.