Since there are certainly a lot of hysterical moments within the series just list the chapter or episode number along with the example if you can, for at least some semblance of organization.
Some highlights include...
Chapter 302 has several moments actually, which is to be expected when the plot is basically, Hayate trying to ask Hinagiku to live with him.
One that stands out is Hinagiku returning home after being frustrated over the whole situation only to walk into her house and find... Hayate getting permission from her mother for Hinagiku to stay at their apartment building. Hinagiku really shouldn't be so shocked considering that her mother adores Hayate.
Another comes after Hayate is incredibly close to getting Hinagiku to agree using a pretty heartfelt and very sparkly expression of how he likes being around her and to see her happy. Since the chapter isn't over and he isn't allowed to succeed yet, he completely fails when Hinagiku (incredibly flustered, mentions that it sounds like he's proposing. Hayate flat out says he was trying to sound like that. And that Yukiji told him to. What sells it is the beat panel right after where he seems to have actually realized his mistake right before the beating.
Adding to Mrs Katsura's contribution is her remark on the dangers of letting an adolescent boy and girl live together.
Mrs Katsura: "Make sure you resist if Hina-chan attacks you, Hayate-kun."
In Chapter 309, Isumi helps Sakuya "become a more interesting person" so that she can understand Nagi's manga. This "training" consists of having Sakuya don a giant penguin suit and dance around comically. Those who recall Chapter 83 will note the karmic Brick Joke.
Chapter 310 focuses on Nagi's attempt to find inspiration for her manga.
Episode 24 of the second season. Wataru's stand-up comedy act is so lame, it's epic. It just has to be seen to be believed.
Alice relates to Nagi and Chiharu the story of being roused from her sleep the night before by a faint voice. The source of this voice was, in fact, a sleeping Hinagiku—who was writhing around and "breathing sweetly". When asked what sort of dream she was having, Hinagiku protests that she was merely too hot.
Chiharu asks Nagi what causes a tightness in her chest. Nagi's answer? After a moment of careful consideration... traps. She doesn't even wait a beat panel before calling out for Hayate.
Hayate: "Oh! Ojou-sama! Well, to be honest... um... uh..."
Nagi: "...You've done it again, haven't you?"
Hayate: "Yes, that's pretty much it..."
In the manga, one butler falls in love with Hayate, who at the moment is under a crossdressing curse. Although initially devastated when he finds out Hayate is actually a guy, he quickly comes around and tries to convince Hayate to travel with him to the Netherlands, where same-sex marriages are legal. (Cue Nagi's Megaton Kick).
The following conversation:
Hinagiku: Now I'll never be a bride...
Ayumu: I'll take you.
Hinagiku: What about Hayate?
Ayumu: That's right... Then how about Polygamy?
In episode eight when Nagi makes Hayate cross dress so she can take photos, which works well since Hayate has a feminine appearance. It's already funny enough that Maria was watching. Then Tama, her pet tiger, sees Hayate in a cat girl costume. He ends up with hearts in his eyes, and then he pounces on Hayate, causing them both to fall out a window. Then Tama starts humping Hayate, complete with the show's man holding a sign that says "can't show" censor. Nagi even wonders if it's because he thought Hayate was a cute cat girl, or if he thought Hayate was a cute guy. It's even funnier if you know that One of Tama's hobbies is looking at male model magazines.
After Season 2 Episode 12, you may never think of "Cruel Angel's Thesis" the same way again.
YMMV on that one. Many people saw that as a crowning moment of awesome with Hinagiku's passionate performance whilst thinking about Hayate, Hayate's resolve to save his mistress even at the expense of his own dignity and the general mood of the scene. The crowds who saw Hayate cross dressing were laughing but still..
The First Episode has a hilarious bit with the Good Angel, Bad Angel, the Devil tells him to give up, then the angel says not to...........and prompt suggests Kidnapping the rich girl for ransom before the Devil starts acting like that's a bit extreme and proceeds to act as the moral compass, compared to the Angel continues justifying the option of Kidnapping.
And let's not forget Klaus's flashback from back when he was a child. Klaus looked like a child with exactly the same face.
In one episode Hayate ends up dressed as a Cat Girl maid by his employer. Naturally, the employer's pet white tiger, Tama, takes a liking to him, and, umm... yeah. The scene is censored, so we're not quite sure if it's actual rape or molestation, but Tama's certainly going through the motions there before Hayate knocks him away with an uppercut.
Chapter 304 reveals that Kotetsu has become a stalker to Hayate when he follows Hayate into the public bath and directly states Ho Yay as the reason why he is there and states that he loves Hayate. Hayate responds by trying to drown him.
Chapter 360 ends with - from Chiharu's perspective - an unconscious Hinagiku, in Hayate's room, on Hayate's futon, with said butler leaning over her. Chiharu makes the obvious assumption and - as the narration is more than happy to point out—she's technically right.
Narrator: "Well, it is true he gave a girl something to drink in order to put her to sleep so that he could do something to her."
Izumi Segawa once walked across her butler (and big brother) Kotetsu confessing his feelings of love at first sight to a forcibly crossdressed Hayate (of course, not realizing that the Cat Girl he was so attracted to was in fact a male). Izumi, knowing that Hayate was in fact male, told the two to "continue, and just don't mind me".
Chapter 350. "You see, if you suddenly open the door, you have an extremely high probability of finding Hinagiku-san changing."
In Chapter 358, Hayate teaching Ruka how to drive a bike. It begins with him asking whether she wants nice or harsh lessons, and from there it spirals into amusement, with Hayate trying to act like a scary coach and using the "you can learn anything if you think you are going to die" approach.
Chapter 383: Ruka has just confessed to Hayate that she likes him and asked him to be her boyfriend. Hayate responds with the same answer he gave Nishizawa-san when she confessed! Ruka then demands a real answer!
And when confessing to him, she also told him that it was her first kiss. Hayate starts thinking about the fact that he can't tell her it was "probably 582nd" for him.
In Episode 7 of the 2012 anime, Nagi and her alleged sister participate in a quiz in order to go to America. Thing is, Fumi is the host and the questions she asks all relate to pretty awkward matters. It just has to be seen to be believed.
What did Kirika want with Hayate? Why did she sent all those Buttlers to fight him? Her Evil Plan was to blackmail him into becoming her butler using Nagi's fortune, because if she got proof that she'd beaten him, Nagi's inheritance would become hers. That isn't funny, you say? That's actually very dramatic, you say? Weeeellll, she was also doing this for the sake of forcing Hayate to wear the ancient butler uniform of a mighty forgotten civilization of butlers. Which is a pink dress, apron, and cat ears. Which he supposedly can also never take off. And when he is forced to wear it, he not only forgets who he is, but also starts acting like a girl. When the student council president sees him like this, she suddenly gets a Luminescent Blush. When Nagi tries to rip the uniform off of Hayate, he stars screaming like a little girl and trying to cover his chest.
Chapter 387 "This is the kind of Manga you are reading". After a lot of build-up and drama Hayate goes to talk with Mikdao about the Inheritance...the meeting is then interrupted by Saki calling Hayate and Mikado repeatedly without a shred of guilt as to what's she's stopping. Eventually Mikado declares the atmosphere ruined and ushers everyone out and resets the date...only to find out Aika's going on a week-long vacation that day as the final member walks out unimpressed.
This is the reality of this manga.
Your mileage may vary on how funny that was. A lot of people were not amused because Hata diverged from the plot just to troll his readers.
Chapter 295 has Hayate dressed as a maid fighting a tentacle-welding robot. Captured and about to be photographed, he warns them he's a guy. See the reaction here.
Not to mention Kotetsu laying claim to him.
That one chapter about a oneshot character called NPC A. His attempts at a romantic relationship with Chiharu are portrayed like a wildlife documentary, and later on, a fight (with commentary!). Plus, it's full of humorous take thats to the otaku stereotype.
In Kyoto the present girls draw fortunes to obtain the "honor" of riding in a Lamborghini instead of a damaged Isumi piloted Helicopter. Every fortune is ridiculous revealing Chiharu as a Yaoi Fangirl, Kayura somehow getting worse than "great misfortune", but the overall loser is Nagi...
Fortune: "LOSER. You will lose. you will spill ink on the manuscript."
Nagi: "What do you mean "loser"!?"
Hayate the Combat Butler has one in Volume 8. Tama (Nagi's pet tiger) has the idea to get Nagi's new kitten kicked out by tearing up her manga and blaming it on the kitten. While the title character tries to convince Tama to stop, the kitten actually does tear it up, and makes it look like Tama's fault. The kitten then goes from extremely cute to highly sinister, with a near full-page close-up and revealing its plan with the telling phrase "Exactly as planned!"(or "Just as I planned!" in the official translation). The karmic payback is funny, but seeing Light Yagami reincarnated as a kitten is beyond words.