They seem to accuse you of warmongering when you capture cities a certain way. If you are attacked, and retaliate, and capture one or two cities of your attacker, most civs will not accuse you of warmongering (there are exceptions, especially if that civ has it in for you already).
At the point where the civ starts offering peace treaties, if you capture a city, you risk the warmonger accusation. The more cities you capture, the more likely this will happen. Once it happens, I don't know of it ever going away.
It can even be gained entirely from defensive wars, if you are capturing cities. What you do with those cities doesn't matter. Declaring war also seems to factor into it. They seem slightly more tolerant of you when you are attacked, as long as you don't become too aggressive.
Of course, there are times when you can be attacked repeatedly, and fend off the battle, and if you move into enemy territory and attack, you risk the warmongering bit. I have never gotten it from simply defending my territory, only for attacking (even if I didn't declare war).
It is one of the risks of war, the more effective your fighting is, the more you risk a warmongering charge.
City-states have more diplomatic weight to them. When you capture or declare war on city states too often, you will have some interesting diplomacy problems. Other civs will look down on you as a warmonger, and city states may refuse any diplomacy with you. Eventually, some of them will declare a permanent war on you. So in general, use discretion when attacking city states (unless you're Attila, because he's made to capture city states and anger people).
You sure about that?
I'm currently in a game where:
- Spain settles near lands that I coveted, declared war on her and took their capitol and two other cities (that I burned to the ground), leaving her with one city.
- After the war with Spain I decommission my entire army, bringing my military rank to the lowest. Carthaginian's leader Dido declares war on Spain, takes her last city and then declares war on me.
I take that puppeted city and burn it and took another city for good measure and burned it.
- After about 50 turns Babylon the runaway declares war on me. After being defensive for about another 50 turns (and refusing peace a couple of times) I liberated a city state captured by Babylon, burn a small city he created and took and annexed his capitol as well as two other fairly sizable cities.
Right now:
Spain is deaded by me and Dido.
Siam is deaded by Babylon.
Arabia is hanging by a thread (Dido and Babylon are harassing him), he doesn't find me a warmonger but doesn't like me either.
Greece is huge and a runaway, he doesn't find me a warmonger and absolutely loves me for some reason.
The Inca are huge, getting beaten by Greece, he doesn't find me a warmonger also loves me.
Dido used to despise me prior to our war and after it but at the moment is my strongest ally. (And doesn't find me a warmonger.)
The only one that is openly against me is Babylon at this point, but everybody else hates him for being the previous runaway.
I've taken the most cities and capitols, yet nobody really hates me.
Even though I had one of the smallest armies pre-Babylon war.