This name has been used occasionally in England since the 12th century. It was not common in the English-speaking world until the end of the 20th century.
In England, it began to be used as a given name after the Protestant Reformation. It was moderately common in the 19th century. It began to rise in popularity again in the late 1980s, probably helped along by characters on the American television shows Friends (1994-2004) and Charmed (1998-2006). It is currently much more common in the United Kingdom, Australia and New Zealand than the United States.
A moon of Saturn bears this name, in honour of the Titan.
In the New Testament Simon is the name of several characters, including the man who carried the cross for Jesus. Most importantly however it was borne by the leading apostle Simon, also known as Peter (a name given to him by Jesus).
Because of the apostle, this name has been common in the Christian world. In England it was popular during the Middle Ages, though it became more rare after the Protestant Reformation.