This is my first post- hopefully I'm not too late- and it's broken up into two questions:

Can distant cities belonging to an empire, say Roman, up and decide to start their own nation, or ally themselves to a nation closer to them? For example, if a Roman empire has two or three cities overseas where there are strategic oil reserves, can those cities- being so far from the influence of their country- decide to ally themselves to another nation that's within a closer approximation?

The second question: Can a defeated nation seek refuge in the territory of another country- either permanently or temporarily? For example (I'll use Romans again) If my Roman empire strikes down the Persians and they're retreating from my offensive push, can they seek sanctuary in their allies' territory?

I'm not sure whether you want historical examples for the events you listed, or whether you see the events you listed as historical examples and want to know whether such events are possible in the game. I'll assume the latter because, frankly, I couldn't say much to the former. ;)

Can distant cities belonging to an empire, say Roman, up and decide to start their own nation, or ally themselves to a nation closer to them? For example, if a Roman empire has two or three cities overseas where there are strategic oil reserves, can those cities- being so far from the influence of their country- decide to ally themselves to another nation that's within a closer approximation?

Yes. Most cities spread the culture of the empire they belong to to the area around them. Certain buildings boost the amount this emitted culture. Cities far away from your empire will be surrounded by the culture of other empires, while generating comparatively little culture by themselves. Eventually, the foreihn culture may be stronger in the city than its own culture. If that happens, there is a chance that the city will change ownership.

The second question: Can a defeated nation seek refuge in the territory of another country- either permanently or temporarily? For example (I'll use Romans again) If my Roman empire strikes down the Persians and they're retreating from my offensive push, can they seek sanctuary in their allies' territory?

Sort of, but not really. In Warlords (not in the vanilla game), a nation can become a vassal of another. If you're attacking Persia, they may try to become the vassal of another, more powerful nation. They give up some of their sovereignty, but in turn the other nation will protect them, and declare war on you.

Get the revolution mod, then cities will join others if they are far away and unhappy

Thanks for the reply. I was listening to this awesome physics podcast called "Physics for Future Presidents" out of Berkeley and a lot of it has to do with oil reserves, coal, and other resources that are politically and economically strategic and for some reason I kept thinking about how these strategies may or may not be incorporated into Civ. Also, are the resources in Civ 4 limited? (Such as oil wells drying up and forests being depleted from lumber mills)

In unmodded Civ4, resources aren't limited. The one exception is forests, which can be cut for a one-time production boost, but are gone afterwards.

Cool, I'll check for mods. Would you recommend any mods for touching up the economic and political realism a bit?