Civilization IV is very good. If you like this sort of game, this is hereby the premier example, in the way that Master of Orion 3 was not.
That said, the world of Civilization is both idiosyncratically different and eerily similar to our own. Some of this stems from the conventions of the genre: in MMOs, you accept that everyone is wearing six backpacks, and in empire-building games you accept that it can take 80 years to walk through a forest.
I have mostly played single-player, and what little LAN multiplayer I have done has been cooperative rather than competitive. I like cooperation. I dislike competition with random online people, for all the reasons you have seen in every other game that randomly matches folks online. Also, multiplayer will be driven heavily by violence, rather than building.
Civilization IV strongly rewards violence. Bombing rice paddies can make gold coins fly into the air. This might seem silly had we not been conditioned by plumbers who produce coins from bricks by jumping into them head-first.
My very best scores have come from being a warmonger. Setting up a small world where I plan to conquer anyone I see gets me a quick game with a fabulous score. Peacefully developing culture and science can also win easily, but at a much lower score. This is perhaps fair, given the history of the world: conquest and domination are rewarded. To win through it, though, you must conquer or dominate pretty much everyone.
If you ever hear that a candidate for office loves games like Civilization, you might want to vote for someone else. These games teach you bad things about how to run a country. Things like “productivity is greatest when government micromanages everyone’s specialization and workplace.” Communism is balanced against capitalism, rather than being the ideology that killed >100,000,000 of its own citizens, and running a theocratic feudal state is a great way to produce an information-age military.
Another notable lesson is that slavery can be very efficient in the right circumstances. For example, say there is not enough food to go around, so much so that people have stopped having sex. If you work people to death building great structures for your further glory, they will start reproducing to replace the slaughtered.
Great artists can live for thousands of years. Not their works, they can actually live that long, especially if you tell them to sleep in one of your cities. By the time you wake them, they will have all transformed into Elvis impersonators.
Aggressive Mongols do not have particularly good cavalry. They get bonus cheap-o cavalry, but being ravenous warmongers does not help them. If you buy the expansion pack, however, they can get better mounted units and even build stables. It can be interesting to start as the Mongols when there are no horses on the continent; that seems to defeat the purpose of being the Mongols.
Stone is a surprisingly rare resource. You might think that you could use those hills or mountains or whatever to get stones, but that is not possible. Only special hills are made of stone; most are of an unrelated substance known as “rock,” which is useless for construction.
Returning to the theme of warmongering, one of the map types is “Terra.” There is a continent or two across the ocean from every civilization. Once you get there, you will find it to be inhabited by barbarians, some with large cities. Your heroic conquest of the New World will involve slaughtering all of their troops and assimilating or razing their cities. There can be no peace: if you let the savages be, they will endlessly send troops to raid your people and burn your farms. You can send missionaries in, but they risk getting slain with little to no benefit if they survive and convert people.
Bureaucracy increases productivity.
Communism increases the amount of food available. This even works for the Chinese and Russian empires. It costs nothing to maintain and reduces corruption.
Okay, officially corruption was banished from the world. Its proxy is now called “maintenance.” This is probably fair, as large empires become harder to keep organized, rather than hopelessly corrupt. All Americans are good at running efficiently running large empires. (Under the expansion pack, that only applies to FDR. George Washington keeps people happy and healthy but loses his organizational skills. There is no Alexander Hamilton to help him with that, so you must tech up to economics on your own there.)
Gandhi’s special abilities let him prevent anarchy when he declares a police state so that he can keep his war machine going at full speed. Also, Indian workers are faster than anyone else. They do not build any faster, they just move faster. Under the expansion set, jails make Indians happier (and also help Gandhi’s war machine).
Sugar makes people happy but not healthy. Something strange must be going on at the grocery, though, because sugar makes you healthier there.
Only Americans can build malls. Oddly, the main reason to build malls is because you are unhealthy. Malls are only available through the expansion set: you must go shop more to have a mall.
Hit Broadway musicals are resources like iron or coal. They are more valuable if you can build malls.
Building a sheep pasture will make your citizens reproduce more quickly. They will also be happier.
Your wonders can become obsolete, but only if you find out about it. For example, learning about calendars makes Stonehenge worthless except as a tourist attraction and learning the scientific method prevents you from having any more monasteries in your nation, but only if you learn the technology. Your neighbors can be telling you about the wonders of calendars for millenia, but as long as you steadfastly refuse to learn how to use them, Stonehenge improves the culture of every city in your empire.
The best way to jumpstart a city is to clearcut every tree within sight of it.
Religion really is the opiate of the people. If you keep building religious structures, people will still be unhappy, but they will not get around to doing anything about it. Also, having many religions in your cities helps your citizens be happier. There is never inter-religious strife.
Within your country, at least. Other nations will grow to hate you for not sharing their official religions, even if you founded that religion, have temples to it all across your country, and introduced it to your neighbors through extensive missionary work.
Religion is also one of the best sources of money in the game. If you have the Church of the Nativity, every Christian Missionary is a chance to get more gold. You can finance huge empires solely on the basis of popular religions.
Everyone listens to the United Nations. If a UN resolution tells you to do something, it is physically impossible to ignore it. When the UN says that no one will build nuclear weapons, everyone quietly ignores nuclear weapons. There is no WTO: the United Nations will never support free markets.
Environmentalism makes everyone healthier but is hideously expensive. Nothing ever hurts or benefits the environment (except maybe nuclear weapons), but environmentalism is still necessary for some reason. Nuclear weapons can cause global warming, but extensive use of coal and oil have no effect. Also, while permanent deforestation is common, fossil fuel reserves are endless.
Rock and Roll is one of the wonders of the world.
The Eiffel Tower causes little broadcast towers to spawn in all of your cities.
I once culturally dominated the world through my Jewish German empire.
There are bears outside. Once civilization gets going, however, all wildlife spontaneously dies off.