Ending a war at the right time can make the difference in a game. Even when I'm the aggressor, my goal is to ultimately to end the war. But as an aggressor, I know that I shouldn't end the war until I have delivered a crippling blow to my enemy. Otherwise peace will be meaningless; my enemy will go full out military build until they can retake what they lost. A good example of a "crippling blow" is taking their capital or taking a valuable strategic resource (for example, their only sources of iron/horses, so they can't really wage a counterattack later). Taking a couple border towns is insufficient to cripple your enemy. So here are my reasons for wanting to end the war as soon as possible (in otherwords, I drive as hard and fast for that crippling blow as I can).
1.) War weariness (as discussed above)
2.) When at war, build all military. But this means your cities will not be developing and you will be falling behind the Civs that aren't at war.
3.) Unit upkeep (you can shrink down your forces after the war if you know they won't be able to strike back to help get your economy back under control)
4.) Time to digest the cities I have captured. During the war, these will be drains on a) your economy and b) you will have to garrison a decent chunk of your attacking units in the city to quell the rebellion and make sure they do not recapture it.
5.) Finally, I often will wage war with an enemy that has a bigger army than me. I win by surprising them with a huge stack of units (12 maybe in ancient times plus a few catapults if I have the tech). While they have a larger army, it is spread out across their civ. If I strike quickly toward their capital, they can't/won't bring it together fast enough to stop my advance. However, by the time I take their capital, I will have used up a good portion of my stack (it does get reinforced as it goes, but not as quickly as it loses troops). What remains will be garrisoning captured cities, and wounded soldiers. Making peace lets me heal up, and does not give them a chance to counter attack now that I am spread thin. And after you have dealt a crippling blow like taking their capital, they will almost certainly take your ceasefire (unless you have razed their cities, in which case they may not).
6.) Once they have been crippled, you should be able to mop them up later. Just accept that in the short term, you will have cultural pressure on some of your captured cities (but this is better then pressure on your key cities right?)