"Operation Final Rest". Resulted in TPK, naturally.
"Operation Fallen God". TPK, all Colonel level soldiers.
"Operation Hot Mother". No, really◊. Apparently Buster is the one at XCOM HQ coming up with all of the operation names. For bonus points that name was assigned to the "Gangplank" mission from the Slingshot DLC.
"Operation Evil Alien". Gee, you think?
"Operation Blind Man". Even worse if you're hit with some of the worst cases of Artificial Stupidity the game had to offer.
"Operation Black Priest"
"Operation: Cryptic Line". Guess someone in Central is fan of meta jokes.
"Operation Twisted Hero". Becomes worse if your rising star is critically injured and then mind controlled into killing their teammates.
"Operation Empty Grave." Don't worry, only 3 soldiers were killed that mission.
"Operation Sacred Empire". Better if the target is a UFO interceptors splashed in Japan.
"Operation Spectral Sentinel". Terror mission with all troopers equipped with Ghost Armor.
"Operation Final Breath". Well, maybe for the aliens and any rookie unlucky enough to not dodge a shot.
The reactions your troopers have to getting Mind Controlled can fit in here.
Any time a Muton successfully intimidates a XCOM soldier, only to promptly get shot and killed by that very same panicked soldier.
Killing a Floater through Overwatch when they are just starting to move. Since they move around by using the thrusters built into their body, the corpse will hurtle across the map until it hits the invisible wall at the map edge. Extra hilarious if they were going up... they never come back down!
Blasting Floaters out of the sky with rockets really never gets old, especially with several bunched together.
On a related note, once in a while Mutons will ragdoll and convulse in a blackly amusing fashion when you put them down, especially in Terror Mission maps. They just flop there and wobble so much.
The same thing can happen with Cyberdisks and other flying enemies in certain maps with 'bottomless pits' (such as the Alien Base, the Skyscraper Rooftop, or a Battleship). The corpse or wreckage will fall off the map, camera in tow... and then the camera has to hurriedly pan back to the action when the corpse/wreck is deleted.
Ragdoll effects reach their full hilarity once the Alloy Cannon is researched. Imagine a Berserker charging one of your team mates only to be sent backflipping over a dumpster by a nearby assault class. It never stops being funny.
Muton Berserkers sometimes wig out and run back and forth - if the squad is prepared this can lead to a hilarious Humiliation Conga as the Berserker trips Overwatch shot after Overwatch shot. Bonus points if some of that Overwatch is from Sentinel-classed Supports.
Some players have taken to just luring the Berserker from one soldier to another, going round and round, until it dies.
Sometimes, it just takes one. With a reasonably powerful enough weapon, an Assault can Rapid Fire a Berserker and hit twice, have it charge at him or her, only to trigger the Close Combat Specialist ability from that same Assault, ending with one dead Berserker.
Another way to deal with them is to move up all soldiers to close range and set them into Overwatch, and have the last soldier finally fire, triggering its movement and then the fire from every soldier in the squad at once. Just like dominoes, but with more lasers and blood.
Alternatively, anything that can fly simply makes fun of the poor Berserkers. Endlessly running at you, never to succeed. Almost makes you feel bad for them. Almost.
Buildings can remain standing even if only a single wall tile remains. Try staying straight faced while that building in the middle of the graveyard is somehow standing with a single row of burnt bricks holding the entire building up as plasma fire is exchanged between the XCOM squad and a bunch of Thin Men.
It's exceptionally unlikely to happen, but non-explosive friendly fire does seem to exist in the game. Imagine - an Assault in low/half cover is outflanked by a Muton two tiles to his south-east, with a Berzerker standing directly next to him, to his north-west, directly opposite the other Muton. The Berserker has two hit points remaining from earlier attacks from the squad. The outflanking Muton raises its plasma rifle to attack - and you can't miss at that range, right? Wrong. It misses. The first shot goes wide, the second two shots smack straight into the Berzerker's face and kill it. Friendly Fire Isn't.
A Muton Elite throws a grenade at a nearby soldier, only to blow himself up. It was then finished off with another grenade.
The naming system can produce some funny moments: A rookie with the last name of Claus saved his team's asses thanks to his medkits. The kicker though, is that upon promotion, it turned out his given nickname was "Santa": "Santa" Claus is now a Colonel bringing 10hp restoring medkits to all the good soldiers each mission.
On a slightly different note, a sniper with the surname Walker. Open reaching Sergeant, the game promptly can give him the nickname...Walker.
Another example, a female sniper with the last name Kerrigan. Her handle once she reached Sergeant? Blades. To top it off, she turned out to be the only soldier to have psi-abilities in that playthrough.
Similarly, with Enemy Within, try getting a Sniper with the code-name of "Cyclops", especially if he's made the first recipient of mutagenic enhancements. Same goes for Tom Taylor if made a MEC trooper. "More power" indeed.
A MEC Trooper that helped out the troopers in a tight spot ends up earning the nickname "Big Daddy".
Anytime an enemy appears and walks right into a Overwatch crossfire is always good for a laugh, especially when it happens to a tough/annoying enemy. They get a little intro then get shredded by an unholy amount of firepower. More Dakka is always the proper solution to your problems.
The Seekers introduce in Enemy Within cloak then move around the battlefield for a fortunate time to strike, decloaking to attack a unit. When they decloak overwatch is triggered. Imagine that there is just one left and you have all your troops clustered within Lo S with one another and on overwatch. The Seeker appears and is shredded by 5 instances of overwatch. Total damage was 31 points of damage on it.
Such as the unfortunate Thin Man who spawned in atop a subway train car during Enemy Unknown's bomb mission and was promptly met by a hail of plasma bolts and an alloy cannon shot. His buddy landed seconds later a few tiles to the south and was promptly obliterated by a plasma sniper shot.
The only thing better than your whole team destroying an alien is a single soldier utterly decimating an alien. For example, during a Council mission, positioning a shotgun-toting Assault on a building that a Thin Man will always jump onto. When the Thin Man drops, activate Close Combat Specialist, and time slowed as he managed to get one foot on the roof before getting blown apart by a Scatter Laser.
EXALT troops sometimes do this as well. But they also come from different directions, which can work well, but might also lead to each EXALT soldier tripping a different Overwatch, resulting in the entire wave getting wiped out.
Alloy SHIVs can provide cover - for your soldiers but ALSO for the aliens. They often run up to hide behind the war machine they're supposed to be shooting at instead. Doubly hilarious if you react by just driving the SHIV away, leaving the alien out in the open and probably feeling like a massive idiot.
There are many ways a Soldier's aim can be reduced to paltry levels in the field. It always seems something out of a military farce film when the Rookie runs up to a weakened Muton, fires at point blank range yet only managing to destroy the wall right behind it, and then being cut down by the bewildered alien.
What can be especially hilarious is having multiple heavies and other troops all go into Overwatch, and watch an alien jump out and trigger an entire squad, who unleash a massive torrent of bullets, lasers, or plasma that pours into the alien...and every shot misses.
Taking advantage of the game's aiming mechanics can lead to some oddly funny moments. Like if a soldier has been heavily wounded (which reduces their accuracy) and has an equally wounded enemy up close. You might have a 23% shot of hitting him with that plasma rifle, but that arc thrower has a 98% chance of success. Ride the lightning, baby!
Occasionally, missed shots actually hit the target visually, but have no effect, prompting loud, angry claims of bullshit from players and sometimes the soldier who fired the shot as well.
Unfortunately for Sectopods, they're not immune to the splash damage from their own weapons. A Sectopod taking on, for example, a mind-controlled Berserker at near point-blank range might wind up causing more damage to itself than the Berserker would have, possibly even killing itself if it took enough damage beforehand.
Once more with the ragdoll physics - punching an Ethereal to death with the Kinetic Strike Module may be the funniest of them all. Normally, they wear long, fancy robes. When they go flying, though, the robes go head-over-heels, making it look like nothing so much as a very proper lady whose dress has undergone a serious wardrobe malfunction.
An interesting note about EXALT's AI is that they are suicidally determined to reach their objective at any cost without any regard to their own safety. This means that placing a MEC with the kinetic strike module in an area that EXALT wants to capture results in a lot of them being sent through nearby walls.