therother already posted his research thread, but let me summarize its findings for those who don't feel like reading the whole thing.

Corruption is caused by distance to capital. If a city is under 15.88 squares from your capital, it will have zero corruption. Over that figure, corruption eats up a percentage of your city's gross income (trade plus farming plus taxes plus mining, but possibly not admin bonuses), which increases linearly until it peaks out at 65% at around 100 squares from your capital.

The only way to counter corruption (other than moving your capital) is law. Each point (5%) of law reduces corruption by an amount equal to 3% of the city's gross income. Note that this means law bonuses are no more useful at the edges of your empire than at its heart, provided they don't reduce corruption to zero—they reduce corruption in proportion to gross income, so they don't reduce severe corruption more than minor corruption.

Note that corruption never earns you money. The corruption heading on your financial summary is actually entitled "Corruption and Other"—the "other" includes things like loot from conquering cities.

A complete list of vices and virtues can be found in Rome - Total War\data\descr_character_traits.txt.

-Simetrical