I really enjoyed starting a civil war by capturing another civilization's capital city. There was one game where I was in the Americas and the Zulus (always crazily warlike and expansionist) had conquered the rest of the world. It looked like they were going to overwhelm me.
So I parked an aircraft carrier and a bunch of transports off of southern Africa and captured their capital city with a surprise attack by overwhelming forces. The entire Zulu empire immediately started a civil war, with half of it becoming the Egyptians. I was unaware of the civil war feature when I did so (wasn't documented in the manual), and it really improved my opinion of the game. I ended up winning because the new Egyptian civilization and the Zulu civilization were too busy fighting each other to send enough against my forces.
The technology capturing feature was great too. I was playing in the Americas one time, and I was hopelessly behind the Chinese. I had musketeers and cannons, while they had tanks. I launched a surprise attack with all the forces I could muster and captured a few of their cities, getting technologies such as the automobile by doing so. I was then able to produce tanks, and ended up modernizing myself by capturing more cities and stealing technology.
I absolutely loved that game.