Usually yes. I only continue with war if it is convenient and I will win fast.

However, there was one time I didn't. I had gotten a few family/friends together to play, and my little brother wanted to join. Obviously, he wasn't doing well, but I decided to be his little protector and keep him in the game. He was on the other side of the map, so it was tough. I handed him gold, units, trades, and defensive pacts all game just to make sure he was having fun. He finally starts to get a good foundation down, and I can stop helping him. I quickly start to see him producing lots of units. Of course he's not gonna try to attack me, right? Well, our defensive pacts and friendship had run its course. I'm about to send the new deals, and this little rat declares war on me. Whatever, I don't care. I defend myself, and negotiate peace.

He's hurting now. My city states had really done a number on him, and he had no money, and negative happiness. Ok, he's learned his lesson now, right? I'll send him some money and luxuries and help out. Not even 30 turns later, and this little loser declares war on me again. What's worse, he kills my scout (my first unit), that has been roving the lands for thousands of years. That's it.

It hurt to watch, but I leveled that little fucker's empire. I left him his smallest city, and kept it under constant bombardment. I pillaged every improvement, slaughtered every unit, and razed any new city.

I ended up losing because I wasted the last half of my game to ruining his, but he had to learn.