Civilization IV has 41 World Wonders (including the seven religious shrines) and 14 National Wonders. Like in Civ3, World Wonders may be built by only one civilization and National Wonders (also known as small wonders) may be built by every civilization. The effects of small wonders are usually more city-specific and you can build at most two small wonders per city. There is no restriction on the number of World Wonders you can build in a city. Each time you finish building a World Wonder, there is a short movie clip showing the wonder being built.
Civilization IV also introduced a new class of buildings called Projects. A few examples are the Apollo Program and The Internet. The main difference between projects and wonders is that projects cannot be rushed in any way, while wonders can be rushed (by forest chopping, gold, etc). Projects are classified into World Projects and Team Projects.
Note: The spaceship parts combined are counted as one project here. Information assumes normal game speed and is correct as of Beyond the Sword, version 3.13.