The infamous "spearman vs. tank" battles that resulted in the icon on Civfanatics - it's a burning tank with a confused Emoticon next to a rejoicing spearman.
Civ IV features Leonard Nimoy narrating a famous quote each time you research a technology. When you research satellites, he quotes Sputnik: "Beep... beep... beep... beep...."
Great People-related anachronisms can be quite hilarious. "Li Bo (Great Artist) was born in Tenochtitlan", while already rather weird, wouldn't have looked nearly as insane if Li Bo wasn't wearing a white Elvis suit.
"Hernan Cortes (Great General) was born in Tenochtitlan!"
The “mech” is a giant bipedal mechanical robot armed with a variety of missiles, Gatling gun arms, laser-beam eyes, and a deadly kung-fu punch. Although not currently found on the modern battlefield, no doubt across the world governments and evil corporations are secretly developing these metal behemoths even as we speak. When these mechs come into service, all of the world’s other weaponry will become obsolete, and humanity’s fate will be decided by a climactic battle between armies of good and evil mechs in the streets of downtown Tokyo. (Assuming that the giant radioactive monsters don’t get us first.)
Kinda dark, when a humble worthless puny pathetic civilization destroyed in the players superior awesome technologically advanced military for the sake of resource or just for -*ehem- "fun", just want to make you laugh maniacally evil.
A great moment while playing II was when the foreign adviser told me to seek other cultures and learn what I can from them. And then I should eliminate them. The military adviser then chimed in with an Evil Laugh.
Loading up a mod that lets you play as Poland and trashing the hell out of the barbarian city of... Aryan.
In Civilization 5, whenever Montezuma is angry with you.
In V, find a city state at total war with a major civ. Gift the city state a lot of highly advanced units, and they may be able to conquer the major civ's cities, keeping the ones with wonders and burning the rest to the ground.