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!
Abduction Mission on top of a skyscraper. Floaters bunched up. Heavy takes a potshot with a Rocket. Two Floater corpses ragdoll off the top of the building and fall off the bottom of the world - endless hilarity!
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 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.
This troper once stunned a Muton at the Alien Base. The Muton slipped down some rails into a bottomless pit. I didn't have a chance to stun another one, yet in the distance I saw the Muton keep falling and falling and falling. Somehow, XCOM managed to retrieve it still alive.
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.
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.
During a Terror mission, after managing to kill a whole pack of Chryssalids except for one who was standing right next to a civilian. It charged the squad, jumping over a counter to do so, and is promptly shot dead by the Colonel Assault with Close Combat Specialist.
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 Berzerker 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.
One time, a Muton Elite threw a grenade to a nearby soldier, only to blow himself up. I finished it 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, this troper once got a sniper with the surname Walker. Open reaching Sergeant, the game promptly gave him the nickname...Walker.
This troper once was handed a female sniper with the last name Kerrigan. Her handle once she reached Sergeant? Blades. Once she turned out to have psi-abilities, I wasn't sure if this was just bizarre coincidence or a legitimate Shout Out, but she definitely became the Volunteer.
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 only thing better than your whole team destroying an alien is a single soldier utterly decimating an alien. During a Council mission, this troper positioned his shotgun-toting Assault on a building that a Thin Man will always jump onto. When the Thin Man dropped, he activated Close Combat Specialist, and time slowed as he managed to get one foot on the roof before getting blown apart by a Scatter Laser. The next three minutes were spent laughing on the floor.
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.
Any time that you kill a Muton with an Alloy Cannon and the corpse goes flying head over heels through the air.
Although it's something you'll be dreading, Dr. Vahlen's reaction when you first see a Chryssalid victim get up and start shambling around is darkly funny.
Dr. Vahlen: As unprofessional as it may sound, he appears to have become...a zombie.
Hearing this line when a Psy-user mindfrays an alien:
Voices in your head!
In one of my very first combat missions one of my guys was standing just outside between a door and a window. I opened the door and told the guy to get inside. Of course, he crashed through the window. It was hard to stop laughing.
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.
Berzerkers are tricky to deal with, because when they are hit they automatically a move to reposition themselves. The best 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.
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!