Earlier today Pat and I were chatting about combat in Civ IV. I was doing my patented backpedal, explaining that combat really wasn't as bad as I thought, that I LIKED seeing my tanks defeated by longbowmen, etc. Somewhere in there we started comparing II and IV, and he asked about how units affect happiness IV. I started to answer, then realized the explanation was long enough to merit its own post, so here it is.
For those unfortunates who never played Civ II or I, your military had a huge impact on your cities' happiness. Under authoritarian governments (Despotism, Monarchy, Communism), every unit you had stationed in a city would turn 1 unhappy citizen into a content one. Under representative governments (Republic and Democracy), the opposite was true: every unit you had which was outside a city (and thus presumably "at war") would cause citizens back home to become unhappy.
This had radical implications for the game, the most direct of which was that you wouldn't choose a representative government if you planned on going to war. Now, with some strategy you could gain a little breathing room - have each city produce one or two units, and construct some strategic wonders and improvements (United Nations, Shakespeare's Theater, police stations), and you could field a small army. Not enough to conquer the world, but hopefully enough to fight back if someone decided to invade. Any more and you needed to switch governments.
This distinction is largely gone in Civ IV. To explain how it works now, I need to first describe how happiness works.
In some ways, Civ IV seems more complicated than its predecessor; it has many new features like religion and promotions that players will need to tackle. However, in one way it is much simpler, and that is that the amount of micromanagement needed has greatly decreased. Happiness was an area that historically required a lot of time to manage; every turn in the late game, I would flip through each of my 30 or 40 cities to make sure they were adequately happy. Not happy enough and they would go into civil disorder, becoming completely useless and possibly toppling my entire government. Too happy and they were spending resources on entertainment that would be better funneled into production and trade. So I spent way too much time making sure the number of happy citizens exactly equaled the number of unhappy.
Civ IV works around this by changing the effects and cases of unhappiness. Most crucially, when your unhappy factors exceed the happy ones, it's only the excess unhappy ones who stop working. Suppose I have a city of size 10 with 10 happy and 12 unhappy factors. In Civ 2, that would mean 0 of the 10 would work; in IV, 2 would stop working and 8 would continue. This means that happiness continues to be an important factor, but is no longer as crucial as before; you can afford to let a city finish what it's doing before addressing it. They also cut down on micromanagement by eliminating the Entertainer specialist. In simple terms, this means that there are no longer short-term fixes for unhapiness; you'll need to tackle a more strategic problem (acquiring a luxurious resource, changing your civics, constructing certain buildings, etc.) instead of a tactical one (calculate how many people to turn into Entertainers).
The factors for unhappiness are also different. In II, every new citizen beyond a certain threshhold was automatically unhappy. In IV, population is one of the factors; larger cities generate unhappiness due to overcrowding, and will need to be met with offsetting happiness factors. There are other factors as well. People will become unhappy if the city is unprotected; if you are at war with a religion this city observes; if you have recently drafted people into the military; etc.
Another factor is "War Weariness." This is roughly analogous to the old Civ II system for unhappiness in representative governments, but is much less severe and more equitable. First, as the name implies, war weariness doesn't immediately kick in. In my war with Elizabeth, nobody was upset for a while; by the end, my largest cities had 2 or 3 unhappiness because of it. Again, because there are no longer home cities, these costs are spread evenly through your empire.
You can treat war weariness in a variety of ways. The simplest is to end the war. You can also build some buildings, noticeably Jails. And your civics can help as well; if you're planning on frequent, long wars, Police State is probably your best choice.
I much prefer this new system, for a variety of reasons. First, it is just more realistic. I like the way unhappiness gradually grows. Consider the United States' recent wars; when they were fought and quickly ended, there was no serious opposition. It is only when they stretch into several years without a clear end in sight that the citizens start getting restless. At the same time, other governments can maintain wars for far longer without serious opposition (consider the 10-year Iran-Iraq war). Secondly, it allows for more strategy. If you want to undergo a long war but will not be producing new units, you might consider a Police State/Free Speech/Organized Religion combo; on the other hand, if you are ramping up to war but are not actively fighting anyone, you'd be better served by Universal Suffrage/Nationalism/Theocracy. Or you can just shift into "Bread and Circuses" mode, funding lavish exhibitions in your Collosseums while your sons die in foreign lands. The point is, there's more strategy involved and it becomes feasible to wage war without necessarily giving up science.
That's a far longer explanation than was requested. Bottom line, happiness is very different from before, and it's possible to wage war without being paranoid about revolting citizens. These are good changes.