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. Actually seeing it in action.◊
Some of the quotes related to technology discovery can be this. One of the most prominent is Civ V's example for Future Tech:
"I think we all agree: The past is over." -George W. Bush
Great People-related anachronisms can be quite hilarious.
"Li Bo (Great Artist) was born in Tenochtitlan", while already rather weird, wouldn't look nearly as insane if Li Bo wasn't wearing a white Elvis suit.
"Hernan Cortes (Great General) was born in Tenochtitlan!"
J Edgar Hoover, Great Spy, in a ninja suit.
Muhammad (Great Prophet) used to establish Christianity in 600BC.
It got even better when the Khmer civilization was added as DLC in Civ VI. Along with an achievement requiring you to build Angkor Wat and a Wat (one possible pick as religious building when creating a religion) in Angkor Wat. The achievement's name? 'Wat Is Love'.
Relatedly, Theodora's diplomacy screen in V shows the Hagia Sophia, even if you built the Hagia Sophia yourself.
Also, if the Byzantines and the Ottomans are in the same game, there'll be a Constantinople and an Istanbul as separate cities, while in reality, those were just different names for the exact same city. The same goes for Adrianople and Edirne.
Gandhi, man of peace and reason, threatening you with nuclear weapons. The devs have kept this stat in since it's so unexpected and so funny to see a war-mongering leader be Mahatma Gandhi.
In Civ V, the AI has various traits between 1~10 scores. Different leaders had different "tendencies" in these scores, which vary between games by 1-2 points in either direction. For example, America's likelihood to conquer city-states is an average 4 but between games can vary between 2 and 6 in value. Mahatma Gandhi's "Use Of Nukes" score in Civ V is a hard-fixed 12!In a 10-point rank system!
Any time another Civ asks the player for help in a war against Gandhi, particularly if the aforementioned Indian hasn't actually done anything of particular threat. Having them declare him as a "Threat to the stability of the world" comes off as hilariously meta. For extra humor, play as a domination-inclined Civ like Bismarck or Montezuma; having someone like Elizabethask them of all people for help againstGandhi is really, REALLY funny.
On a darker note: when a humble worthless puny pathetic civilization gets destroyed by the player's superior awesome technologically advanced military for the sake of resources, or just for -ehem- "fun", it just makes you want to pull a maniacal Evil Laugh. Even when they instigate and crash their army into your superior defenses, it can still evoke this. Having too many delegates in the World Congress and taking unfair advantage of it is also pretty funny.
"You have discovered scrolls of ancient wisdom." "Robotics" (Or for some meta fun "Writing")
In a similar vein, in Revolution, moving into the space where a friendly village is has a chance of finishing research on whatever technology you're working on discovering. Whatever technology. Even "Space Flight" or the nebulous "Future Technology". There's a lot more going on under those straw roofs than you might guess.
On the opposite end of the spectrum, you might defeat a Barbarian Village and be rewarded with a "strange sea-going craft": The Galley. It's the weakest watercraft both offensively and defensively, it's tied with the Submarine for lowest Movement ability, and it's the only one that cannot venture into deep water. Kinda makes you wonder how he'd react to Cruisers and Battleships... which might very well be around when you get this reward.
Some strategic resources can only be seen rather late into the game, sometimes where you least expect. For example, finding out the location of your first uranium deposit is the same place as your first farm.
In Civilization II, the Entertainment advisor in the Modern era is an Elvis Impersonator. In ancient times, you instead have... the same Elvis Impersonator, but wearing a toga. And he'll always refer to you as "King", complete with a short pause before the title and striking a very Elvis-like pose as he says it.
Speaking of the military advisor: While all the advisors were hammy to some degree or another, the military advisor is a Boisterous Bruiser without equal who absolutely lovesChewing the Scenery.
Loading up a mod that lets you play as Poland and trashing the hell out of the barbarian city of... Aryan.
After this Easter egg occurs, you can find a unit called Jaimo who is based off of one of the staff for Civ III. He attacks by slapfighting and does disco dancing when he wins.
If you found enough cities that the game runs out of names, it cycles through the list again but with "New" appended to them. This means it's possible to have two New Yorks and two New Orleanses - not to mention New New York. Civ III takes it further, though: instead of "New Instanbul", the Ottomans get "Not Constantinople". (And yes, the Byzantines get "Not Istanbul" instead of "New Constantinople".)
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...."
In Civ Rev, Great People are spawned under certain conditionsnote when you break culture thresholds and certain gold thresholds, as the first-discoverer reward for certain techs, and when you discover the School of Confucius, and each Person spawned is related to a tech. The Great Person related to the Superconductor? Leopold Stokowski.
Civ V-specific
The names of many of the achievements.
If you fail to build enough wonders before the other cultures do (once another culture finishes a wonder, you lose the chance to finish yours), you earn an achievement called "Seriously?!"
A (never implemented) achievement was called "Cat Fight". You would get it by being a female leader and declaring war on every other female leader on the map at once.
What's the achievement for killing an enemy spy trying to steal a technology? Whack aMole.
If you win a science victory as Poland, the achievements will tell you that, yes, Poland can into space.
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.)
When Suleiman is defeated, he says "For the sake of my beard and my belly, how could this happen?" Even funnier if you speak Turkish, since his voice actor speaks with a very colloquial, very Modern Turkish in a very Large Ham way, making him hard to take seriously for Turks.
Virtually every leader has some comment whenever you attack them. But Pacal? He just laughs at you. Funnier still, is if you get a generic "You fool, you have made a terrible mistake," message when you do so - as if the game is warning you for declaring war against him.
What makes this even funnier is that he follows it up by suggesting you can beat the Indian troops through "passive resistance" (a reference to Gandhi's protests against the British occupation of India). It makes it sound like he's asking you to just sit there and do nothing while his troops conquer your territory.
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.
A bit meta, but the fact that Siam's unique building (the Wat) was involved in an infamous early glitch, and is still abused along with Legalism in some strategies makes its name all the more amusing ("Four free universities. Wat.").
In multiplayer under the diplomacy tab, there is an easily accessible "Declare War" button right next to each player's name. This often results in accidental declarations of war.
When you finish building a wonder it will show up on the map near the city that built it. This is a cool detail, but it turns out the game does not into account anything surrounding the city when placing the wonders model. This can result in things like the Eiffel Tower being embedded in the side of a mountain or the Pyramids of Giza being built off the coast of the city half submerged in water.
Even with the option of having Chandragupta as the leader on India, Gandhi's nuke-happy personality creeps in to a Chandragupta-ruled India, as you can get the achievement "I Thought We'd Moved Past This Joke" if you successfully launch a nuke when playing as Chandragupta.
Several of the achievements are all about performing actions that highlight the absurdity of the game mechanics, such as airdropping a unit of ancient-era slingers. One of them hangs a lampshade on the lot - the achievement for having a Roman Legion clear some nuclear contamination is "Missed that day in history class".
Poland's culture-bomb ability will destroy any incomplete wonder occupying a stolen tile. The name of the achievement for doing so? "You Are a Terrible Person".
The leader screens in Civ VI have a couple funny moments as well.
Denouncements are usually unvoiced, meaning all the leaders are just doing angry poses and/or grunting at you. This leads to things like the sight of Her Majesty, Queen Victoria... throwing a tantrum like an upset teenager.
Most leaders look at you fondly when you have a declared friendship/alliance. Meanwhile, Phillip II goes into a silly pose with his wrist on his hip and what can only be described as a smarmy grin.
On the rare occasion that Gandhi declares war on you, this is what he'll say:
Upon first meeting Frederick Barbarossa, he introduces himself by listing all of the lands he rules over — Germany, Italy, Burgundy... — before seemingly forgetting the rest and waving it off, saying, "and many, many more."
Kristina's "Bibliophile" agenda makes her hoard as many Great Works as possible, and dislike other civs who compete with her. Judging by her Agenda Disapproval quote, it's because she thinks you won't properly appreciate the art like she would, and are instead just collecting art because it looks pretty.
Kristina: I presume you only view art as good when it ties together the aesthetics of a room, you philistine dog.
Many of the leaders will respond to aggression with condescension or insults. Kupe does them one better: declare war on the Maori, and not only will Kupe completely fail to take you seriously, but he'll ruthlessly patronize you for even trying. Note that when he says "good job, mate," he gives the player a big, cheesy thumbs-up.
When relations are sour between Kupe and the player, he will be hunched over and occasionally perform the pūkana - i.e. stick his tongue out as far as possible while staring you in the eyenote a gesture done in several haka dances. In war-related dances they may symbolise a threat to eat your enemies. While an effective threat, it also looks quite silly.
By contrast, there's Kupe's offer of Friendship. While most other leaders are respectful or downright flowery with their prose, Kupe's just much more casual with it.
"There are worse people in the world than you, surely. Mind if I tell the others you're not a complete jerk?"
Offer an already-angry Hojo Tokimune a terrible deal, and he'll do a beautifully animated Double Take.
Several tech descriptions (like for Sanitation) are from Monty Python. That's funny enough in itself. Now imagine Sean Bean of all people reading the "What have the Romans ever done for us" quote.
Whoever wrote King Arthur's Civilopedia entry seems to be aware of all the Monty Python references:
He could, despite popular depictions, count to three without immediately leaping to five and appeared to have no unusual issues with rabbits.
City-states will go to war together with their suzerain (i.e. the civ with the most influence over them). Nothing prevents you from sending further envoys to a city-state whose suzerain you go to war with, so in longer wars, city-states may switch sides several times. In Rise and Fall, becoming the suzerain of a city-state you were previously at war with also gives you era points, making it even more attractive to win city-states over this way.
Some of the Historic Moment announcements. For example:
If you found a religion but aren't the first to do so:
(Insert Religion Name) is the true path of salvation! Please ignore all those other ones!
For building a high-adjacency Commercial Hub:
They say that people are drawn to the Commercial Hub of (City name) just for the excitement of buying and selling in the market. But the money is pretty good, too.
For your first Seaside Resort:
Our first Seaside Resort opens in (City name) to the delight of all our people, except for one small child whose snack has been carried away by a seagull.
One of the secondary agendas a leader can have is trying to have the highest Tourism. If you're transgressing this agenda, you get this message:
I know the world is beating a path to your tourist sites, but be warned! Our people possess blue jeans and rock music and we are not afraid to use them.
Frederick Barbarossa doesn't mention any gifts, instead just using his delegation message to brag about his many titles. Which means he either got so wrapped up in tooting his own horn he forgot to tell you what gifts he brought, or he didn't even bother sending any in the first place.