Culture

§ In Civilization IV, "culture" refers to a civilization's accomplishments in literature, the arts, and so forth. Civilizations with high cultures are respected or envied by lesser civilizations. These civilizations tend to intellectually dominate their neighbors, which can be very useful when two civilizations are striving for control over limited terrain.
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Generating Culture

§ Culture is generated in Cities, and each city has its own cultural value. A new city, containing just a few citizens intent more upon survival than on anything else, generates very little culture. But once the city grows and begins to construct Buildings dedicated to religion, arts, literature, and so on, its cultural output will increase. The city can further increase its cultural output by creating certain Specialists, as well as by using Great People. However, the greatest increase in culture can be gained through the construction of Wonders.
§ Culture Button
§ Once you have discovered the Drama technology, you can devote a certain percentage of your civilization's commerce to culture using the Culture Button. This can allow you to create culture in cities that have no buildings in them (although it may be expensive to do so!) The Culture Button also provides Happiness in addition to culture; see the related Civilopedia entry for more details.
§ Building Culture
§ After discovering the Music technology, you can devote a city's production to the creation of culture. The city will not build anything, but it will produce culture.
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Culture and City Defense

§ People fight harder when defending particularly holy, beautiful, or otherwise culturally-important cities. To reflect this, cities with high cultures get a "city defense bonus." This bonus increases as the city's culture grows. See Cities and Combat for more details.
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Culture and Borders

§ A city's cultural value determines the size of the land it dominates. See Borders for details on this important effect.
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Cultural Conversion of Cities

§ If a culturally-superior city is near to another civilization's city which has little going for it culture-wise, the superior city will tend to dominate the inferior. This usually results in the superior city gaining control over the land between the two cities, and sometimes of all the land surrounding the inferior city. This can lead to starvation and, in extreme cases, of the inferior citizens Revolting from their civilization and joining the superior city's civilization.
§ A city must revolt twice before it flips to the dominating civilization's control. The first time that the city revolts, it will eventually return to the original owner's control. The owner may then try to pump up the city's culture to avoid a second revolution: but if the owner is unsuccessful and the city revolts again, it will flip and join the dominant civilization's empire. When a city "flips" to your control, you automatically gain all of that city's buildings and great wonders, making this a far more profitable (if perhaps less satisfying) way of conquering a city than through direct force of arms.
§ There is one exception to the above rule about cultural conversion: a city that has been captured militarily will never flip back to its original owner, no matter how much cultural pressure the original owner brings to bear (although it may be near-useless to the conqueror due to constant revolts).
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Barbarian Cities

§ Barbarian cities have cultural values just like other cities. They too can be converted through cultural dominance.