I sometimes turn off Espionage, because it is kind of a hassle to deal with, but when I don't... I LOVE to send 2-4 spies repeatedly into border cities I covet (such as holy cities or cities at chokepoints) to spread my culture until it peacefully flips to my control. If you are creative, this is even better, because you are more likely to have some influence to most border cities. Once you have 0% (which is to say, something, but not yet 1%), you can start the culture flip. Before too long, you will start seeing tiles become yours... then some riots in the city... and then, whammy... its yours. Great little tactic. No diplomatic strike from open combat either.