Religion has always played a role in the Civilization series but in Civilization IV that role is being boosted, religion now shaping the way your civilization develops. In total there are seven religions in the game, these unlocked via research. Once unlocked, a religion spreads through your empire and you can use it to help manage happiness, gain gold and create Great Prophets.
Explaining the role of religion in Civilization IV in greater detail is Barry Caudill, producer on the game at Firaxis...
"Religion has always played a critical part in human history. Through religion, man has sought to make sense of the universe around him and to determine his place in it. Religion has inspired, enlightened and ennobled man; in its name men have erected beautiful buildings, written books of great wisdom, and made music of surpassing beauty. In its name men have also murdered and enslaved their fellows. Given the importance of religion throughout history, it seemed fitting that we should try to address it in Civilization IV.
"Through our tests, it was determined that the optimal number of religions for gameplay purposes was seven (a number that seems to come up quite often when designing versions of Civilization). We then set about making a list of seven important and recognizable religions. After a lot of deliberation and more testing, we narrowed the list down to these: Buddhism, Christianity, Confucianism, Hinduism, Islam, Judaism, and Taoism.
"If you are the first to discover the technology associated with a religion, the religion is founded in one of your cities. Religion can spread passively throughout your cities and even into neighboring cities belonging to your opponents. Establishing trade routes can help spread your religion faster and farther. Certain religious buildings can also help this passive spread but if you want to move the process along, you will want to create missionaries. Missionaries are units that you can move to another city (your own or an opponent's) and attempt to directly convert that city to your religion.
"In addition, having cities that have converted to your state religion can give you monetary and happiness bonuses. You can also get some line of sight benefits, and provide yet another interesting decision in a game already filled with interesting decisions."