I was just thinking about this the other day in a game...
Civ3 allowed you to bomb and target arty to enemy (and your own) tiles which allowed for some interesting tactics. First there is the obvious resource denial - take out their access to aluminum, rubber, oil etc. You could also starve large cities by taking out tile improvements, or simply hamper the AI's ability to reinforce a city by removing roads leading to it. It was nice, but since it was all ranged, it was pretty one sided...plus the AI did a much worse job of it than humans.
At first I missed it, but with all things considered, it doesnt really have a place in C5. To do something similar in C5 take strong troops with the pillage ability, send them in to pillage key improvements then withdraw to heal if necessary. This entails more risk than ranged pillaging since the city and nearby troops could overwhelm some of the pillagers.