What are the effects of Civilization V responses to other leaders?

With the exception of diplomatic responses that can be taken as promises and some of the ones relating to city-states, they're just flavor text.

The "promise" ones are stuff like you saying you aren't planning to invade or expand near them. Breaking promises makes all civilizations trust you less, not just the one that you're talking to.

The city-state ones that effect things are ones like where they attack a city-state under your protection and you can choose to ignore it or stand firm. I believe hovering over the options actually tells you, in this case, what they do.

There's some more information on this dynamic on the civ fanatics forum.