Pretty much any of the 'two-man routines' between BJ Hunnicutt and Hawkeye Pierce:
BJ: [to Hawkeye] Your gun, sir.
Potter: Is it loaded?
BJ: I filled it with water myself.
Hawkeye: Look out everyone, I shoot to drown!
In the aforementioned episode, Hawkeye has two other bits involving serious wordplay to show how much he detests guns.
Wasn't in that episode (it was in "Officer of the Day" instead), but:
Hawkeye: I'll carry your books, I'll carry a torch, I'll care a tune, I'll carry on, carry over, carry forward, Cary Grant, cash and carry, Carry Me Home to Old Virginia! I'll even hari-kari if you show me how! But I will not carry a gun!
And then later in "Hawkeye Get Your Gun"
Hawkeye: I'll clean their wounds, heal their wounds, bind their wounds, but I will notinflict their wounds!
Col. Potter's sleep-medication-induced rambling anecdote about prickly heat... over the PA system while Margaret, who has that condition and wants to keep quiet about it, is trying to explain the situation delicately. What she didn't know is that Klinger has finally reassembled and reactivated the PA system after needlessly dismantling it for practice. When she finally hears the rest of the camp laughing and realizes why:
Houlihan: Wait a minute, is this stupid PA on? Klinger, you idiot!!
Klinger: Major, no! It took me 3 hours to fix this thing- *SMASH*
In "Dr. Pierce and Mr. Hyde", Hawkeye stays awake for three days straight, and becomes so sleep-deprived that he stumbles into a lecture by Frank and asks him why the war is happening ("Was it something we said?"). Frank replies that the North Koreans envy the American way of life; Hawkeye concludes that the war might end if the North Koreans had indoor plumbing, and concocts (and partly carries out) a plan to ship the latrine (and the visiting general inside it) to the North Koreans to end the war.
Trapper: What happens in the event that figure 'A' is attracted to figure 'B' and wants to get married. But figure 'A' is already married to figure 'C' and figure 'B' is engaged to figure 'D' but figure 'A' can't keep his hands of figure 'B' because she's got such a great figure."
Radar: Sir, do you suppose that sometime you could give us a talk about VD?
The episode "Tuttle", enough said. Especially Hawkeye delivering a eulogy for Tuttle at the end of the episode. The look of horror on his face when Henry suddenly asks him to deliver the eulogy is hilarious, but then Hawkeye manages to pull it off.
"98 degrees plus 98 degrees equals 196 degrees."
In one episode BJ pulls a prank on Hawkeye and Charles that involves Charles frequently getting pantsed and Hawkeye getting the blame and almost turned into a camp pariah. When Hawkeye and Charles figure out what BJ is up to they fire back in grand style: they strip BJ while he's asleep, stick him and his cot in the nurses' tent and nail his blanket to the cot so that he can't use it to cover up. Then they fake an announcement of incoming wounded to ensure that BJ comes outside, where Hawkeye and Charles are lying in wait with an audience of nurses and enlisted, and a camera to capture it all for posterity.
After being told by Klinger for the umpteenth time that I-CORPS won't replace her broken footlocker because it wasn't damaged in combat, Margaret calmly borrows Winchester's hunting rifle, walks inside her tent and then shoots said footlocker.
Margaret: There I was, alone in my tent! Suddenly, a sniper leaped out at me, and fired two shots! Bang! Bang! Without hesitation, my valiant foot locker threw itself into the direct line of fire, giving its life that I might live!
In a fifth season episode, Klinger was pouring what appeared to be gasoline over himself in another attempt to get a Section 8. Colonel Potter calls Klinger into his office to try to talk him out of it, and whispers something to Radar behind Klinger's back. A minute later, Klinger rejects Potter's offer and resumes pouring the "gasoline" over himself. Then, he suddenly realizes something. Klinger spits out the ''real'' gasoline, then yells "Who put gasoline in my gasoline?!?" He gets up and runs into a nearby shower tent. A nurse runs out, screaming and covering herself with a towel.
Col. Henry Blake unknowningly giving a discharge to a sheep.
Henry (upon finding out): Private Charles Lamb?
'The General Flipped at Dawn'. Eccentric, racist General played by Harry Morgan, the same actor who later plays Col. Potter.
His breaking out singing, "I Wish I Were in Dixie" will bring a tear to your eye.
"We will now leave one by one in order of departure."
In the Season 4 episode 'The Gun', Radar is blamed for the loss of a colonel's personal revolver (actually stolen by Frank Burns). Radar eventually gets drunk and confronts the colonel; at the same time Frank tries to return the gun...and shoots himself in the foot.
Radar:You better believe it, Or I'm dead where you stand mister... [points teddy bear at colonel like a gun, at which point we hear Frank shooting himself in the foot] MY BEAR WENT OFF!
The stunned look on his face really sells it.
"YOU TELL 'EM, FERRET FACE!"
"Frank Burns eats worms."
Klinger's (fake) letters from his family. Especially the scene in which Henry Blake reads from an extensive group of letters requesting that he be given a discharge because various people are dying or pregnant. In the last, half the family was dying, the other half was pregnant.
Blake: Klinger, aren't you ashamed of yourself?
Klinger: Yes, sir. [beat] I don't deserve to be in the army.
"Hey, Henry, isn't that your desk?" "It just keeps going up, and up..." "To a far, far better place I'm sure."
Throughout the episode 'Dear Sigmund', pranks have been played on just about everyone by BJ Hunnicutt. At one point, Sidney the psychiatrist exits the tent to find Frank digging an air raid shelter to hide in, just in case. Towards the end of the episode, Sidney comes outside to find BJ whistling as he fills the shelter with water. He asks if Sidney wants to help, and tells him to shout 'air raid' as loud as he can. He does so, and Frank runs out of the tent in his long underwear and dives for the hole. Hilarity Ensues.
In "None Like It Hot", Hawkeye and BJ have ordered a collapsible bathtub to beat the summer heat, initially planning to keep its existence a secret between themselves. However, word quickly spreads, first to Charles, Fr. Mulcahy, and Margaret, and finally to the entire camp, until Col. Potter imposes a ten-minute limit on use of the bathtub and there are frequently over a dozen people queueing up to use it. Halfway through the episode, a fight breaks out between Sgt. Zale and another enlisted man over their place in the queue, and Charles - previously last in line - proceeds to stroll past the queue as it dissolves into a crowd watching the fight, all the while muttering "Hey, there's a fight over there!" and similar phrases, until even the current occupant of the tub exits the bath tent to watch the fight. A smirking Charles promptly disappears into the tent for his ten minutes in the bath.
Klinger's attempt to get a Section 8 in this episode involves wrapping up in fur coats and long underwear and drinking hot chocolate in spite of the heat; Potter decides that if he keeps the charade up for several days, he will give him a discharge. With just hours to go, Klinger snaps, strips off his warm clothes, and charges into the bath tent - causing a screaming Margaret to rush out of the tent, wrapped in a towel.
Hawkeye in the tub. For the record, he's sitting in pre-op, giggling like a fool, singing, and squeezing a rubber ducky. Meanwhile, BJ is outside, trying to dissuade Father Mulcahy from coming in. BJ is talking calmly to the Father as if nothing's wrong. You can clearly hear Hawkeye laughing hysterically in the background, along with the quacking of the duck. When the Father finds out, he chides them but acknowledges that they need to hide the tub. Then Margaret bursts in. Bear in mind that all Hawkeye has on right now is a small towel.
Margaret: I want it!
Hawkeye': Women often have that reaction when they see me naked.
The entire episode of "Joker is Wild". After accepting a dare from Hawkeye, who had been unfavorably comparing BJ's pranking ability to his old friend Trapper's earlier, BJ proceeds to play an elaborate prank on him. It at first seems BJ is pranking everyone else in a rampant gag spree, however the others are actually in on it the entire time. Hawkeye was the ONLY target. By the end of the day, Hawkeye is so paranoid he ends up surrounding his cot with barbed wire fencing and keeping a rifle at the ready, refusing to sleep. His expression when the The Reveal happens is priceless. Doubles as a Crowning Moment of Awesome.
When Margaret needs a pregnancy test, Radar allows his rabbit to be used, provided the doctors not kill it. Hawkeye and Margaret manage to perform surgery on a rabbit despite having no experience or idea of what they're doing. Margaret thanks him afterward, and Radar says, "That's all right, Major. You'd've done the same for her."
Hawkeye driving the entire mess tent into revolt after they serve liver or fish for a week straight. See it in all its glory here.
Hawkeye & Trapper sitting in the Swamp wearing gorilla costumes, acting nonchalant. Even better is when Frank reluctantly asks for the pair to operate on his hernia, Hawkeye replies that he needs to consult with his colleague. The two begin hopping around, making gorilla noises, until Hawkeye turns to Frank, drapes his arm over Trapper's shoulder and says that "We'll do it—me and the missus."
Bonus points for Trapper moving into the "Thinker" pose.
Anytime Radar feigns innocence, despite being probably the most savvy person in the unit.
Frank:(Walks into office) What are you doing here?
Radar: I was drafted, sir.
Hawkeye upon learning about the (false) ceasefire from General Clayton.
Hawkeye: General Clayton this is Benjamin Franklin Pierce, look I realize youíre a general and Iím just a captain but I want to have your baby.
One episode has Hawkeye, Trapper and Frank off to pick up some wounded that are being returned to them. They are warned that they are not to bring weapons, at the risk of losing the wounded in question to prisoner camps. Frank, being Frank, sneaks along a small handgun, giving himself away when he goes for it in response to a misunderstood gesture. The man in charge of returning their wounded is royally pissed off at this breach of contract and demands that Frank produce the weapon. When he does...
[laughing incredulously] What the hell is that!?
Of course, looking at it, the gun is so hilariously tiny that Hawkeye deeming it as something that would have come out of a box of cracker jacks is appropriate. For reference: Frank holds the gun up with two fingers.
"Hey Doc": Potter gets a tank sent to the 4077th to scare away a sniper. Frank brags to Maj. Houlihan how well he can drive said tank and decides to take it for a spin. He does not do well. At all. The tank goes bonkers and drives through half the camp (literally), including flattening the Swamp (sending BJ combat-rolling out the back through the mosquito netting and running for it), the rampage finally culminating in Potter parking a jeep in front of the tank and ordering Burns (who has no idea how) to stop. He gets out of the way, but the jeep does not. As the flattened jeep's horn continues blaring, Potter draws his pistol and shoots'' it to put it out of its "misery" like you would a horse.
Bonus points: Potter is former Army cavalry and earlier in the episode, he refers to tanks as "Today's Cavalry". It's the punchline to one episode long horse joke.
Even better: It's probably a reference to one of the famous Bill Mauldin's WW 2 cartoons, where an old cavalry Sergeant shoots a broken down jeep with tears in his eyes.
In the episode "I Hate a Mystery", Henry is turning the Swamp upside down looking for stolen property. Turning up nothing, he comes to the stove and accusingly asks Hawkeye and Trapper what's in the stovepipe, to which Trapper replies, "Soot." Not believing him, Henry disassembles the pipe and looks into it—getting a face full of soot. It's a pretty standard slapstick cliche, but what makes it funny is Hawkeye's reaction, laughing so long and hard it's impossible not laugh with him.
It's even better because Radar is obviously trying not to laugh, and Henry's actor is corpsing a bit himself.
Hawkeye and Margaret's kiss in Goodbye, Farewell, and Amen that goes on...and on...and on, while Potter, BJ and Charles stand awkwardly and try to look anywhere else. Colonel Potter's reaction in particular is hilarious.
Klinger to a little Korean girl in camp in "The Abduction of Major Houlihan":
Klinger: This is what happens to you when you don't eat your vegetables.
In "Crisis," set during a cold snap while supplies are running low, people are stealing from Henry's office in order to keep fires burning, including slowly dismantling his desk over the course of the episode.
Henry: Radar, am I getting taller or is the room shrinking?
Radar: Well, somebody cut the legs off, sir.
Henry: Aw, that's dirty pool.
Radar: Well, they'll burn anything to keep warm, sir.
Henry: I know! But to cut off a man's legs, and steal his drawers!
BJ's introduction to Frank Burns.
BJ: What say you, ferret-face? (falls down laughing in drunken stupor)
The escalating prank war between Margaret and BJ and Hawkeye in "An Eye for a Tooth", orchestrated behind the scenes by Charles who is playing both sides.
In "Potter's Retirement", a mole is sending reports to the Inspector General about Col. Potter and he's debating retiring as a result. Hawkeye and BJ confront Charles, assuming that with his grudge against Potter he'd be a logical informant. Charles's response is as always, erudite and hilarious.
Charles: There are no informers in my family! Winchesters do not spy! [beat] We do on occasion hire them...
The staff's reaction to Klinger's redecorated room. Klinger brings Hawkeye and Margaret into the office where Potter, Charles, and BJ are waiting, and the two react with Stunned Silence...until BJ, obviously trying to avoid laughing, lifts up a massive conch shell that he found in the room. Then everyone loses it.
Bottle Fatigue. Hawkeye tries to quit drinking temporarily after seeing just how much alcohol he's been consuming. The first morning, he comes in singing loudly while BJ and Charles are hung over and trying to sleep. Charles's reaction is priceless.
Charles: Pierce, you remind me of a dog I once had. He too was cheerful in the mornings, so I gave him to a family of immigrant Japanese and they ate him.
Klinger: (jumps out from behind a corner, shaking what looks like flour at Col. Potter and Radar) Um-dallah! Moo-goo-gai-pan! Hear me, oh spirits of darkness! beatpoints at Col. Potter That's the guy.
In one episode, Col. Potter and Hawkeye have to instruct Fr. Mulcahy, over the radio, in how to perform an emergency tracheotomy. The Fr. succeeds and signs off over the radio.
Potter: Well, what do you think?
Hawkeye: I think I'm an idiot. I came all the way to Korea to do surgery when I could have stayed at home and phoned it in.