Do buildings have upkeep costs?

[RoyalGuard]

Like the title says.

Another question is it possible to keep most of your cities happy (that is if you have a lot of cities, and without using mods).

[Publius]

Buildings do not and a good way to make the people happy is to focus more on economy and less on your military. Not always as fun, but effective

[RoyalGuard]

Meaning that I should build more economy type buildings rather than military buildings?

[Publius]

Correct. Heres a quick guide to happy towns (without cheats). Very early on focus on such things as paved roads, ports, and temples - dont worry so much about getting "elite" units. As you slowly expand your empire, make sure that your inner, protected cities are filled with more auxilia types (town watch or militia hoplites are perfect for this). They are low upkeep and can still defend cities fairly well. All of your regular infantry should be sent to the frontier. Many people do not do this because they dont get the nice elite units right off of the bat. But if you stick with an economy based strategy, eventually you will have so much money coming out of your arse that you wont be able to produce elite units fast enough.