The entire first chapter. The Muggle Prime Minister's reaction to Fudge and his antics is absolutely hilarious.
Especially funny when you realize that the Muggle Prime Minister at the time was John Major. Or, in other words, the least funny, greyest man not just in British politics but those of any other country, the man who ran away from the circus to become an accountant, whose most charismatic moment was squeeing at his old concrete house in Birmingham, is now having a conversation with the Minister of Magic.
And the Prime Minister before him, aka Margaret Thatcher, threw Fudge through a window.
Snape's retort about Ron's Apparition failures isn't bad either.
Gryffindor's second Quidditch match. In layman's terms: Gryffindor's goalkeeper tries to teach the Beater (who hits cast-iron balls called Bludgers at other players) how to play his position, inadvertently using Harry as his object of demonstration. He wakes up hours later in the Hospital Wing, with a cracked skull.
Madam Pomfrey: I'm keeping you in overnight. You shouldn't over exert yourself for a few hours. Harry: I don't want to stay here overnight, I want to find McLaggen and kill him. Madam Pomfrey: I'm afraid that would come under the heading of "over-exertion".
Then shortly afterward Ron casually mentions that Ginny had stopped by while Harry was unconscious. "Harry's imagination immediately went into overdrive, swiftly constructing a scene in which a tearful Ginny confessed her feelings of deep attraction while Ron gave them his blessing..." Only to have it implode when Ron mentions she was just wondering why he was so late for the match.
"But the more I hint I want to finish it, the tighter she holds on. It's like going out with the giant squid."
Try not to laugh when Hagrid and Slughorn get hammered and start singing a sad song. You will fail.
Slughorn:And Odo the hero, they bore him back home, to the place that he knew as a lad, they laid him to rest with his hat inside out, and his wand snapped in two, which was sad. Hagrid:(about how good people die young) ...terrible. Slughorn: Sorry. Can't carry a tune to save my life.
"We're not going to be asking, 'Excuse me, are you the imprint of a departed soul?'"
What about the "Roonil Wazlib" scene?
Snape: This is your book? Harry: Yeah. Snape: Then why does it has "Roonil Wazlib" in it? Harry:(beat) That's my nickname. Snape: Your nickname. Harry: That's what my friends call me. Snape: I understand what a nickname is.
Peeves blocking a hallway and claiming he won't allow anyone to go through unless they set their pants on fire. Harry and Ron just take a different route. Five minutes later, Neville comes in, smoking and looking for a pair of pants to change into.
Dumbledore's wineglasses tapping the Dursleys on the head for attention.
Harry's pinning after Ginny results in a lot of these:
"It was natural that he would be concerned about her. Natural that he would want to look after her. Natural that he would want to blast Dean into a million pieces for kissing her...no, he would have to control that particular brotherly instinct."
"Ginny kept popping up his dreams in ways that made him devoutly thankful that Ron couldn't perform Legilimency."
Snape's deliberate tweaking of Bellatrix in the second chapter, where he answers all her suspicions about his loyalty, while almost constantly insulting her:
Snape: "Of course you weren't a lot of use to him [in Azkaban], but the gesture was undoubtedly fine."
Ok, I cannot be the only one who laughed when Fleur at firsts Mrs Weasley that Bill will still love her after he was attacked by Greyback and then when she does understand what Mrs Weasley was inferring raves about how she doesn't care about how Bill looks and that she's "Good looking enough for the both of them!"
For the film:
After Luna fixes Harry's broken nose:
Harry: How do I look? Luna: Exceptionally ordinary.
Prof. Slughorn: Harry?! Harry:(same annoyed tone) Sir?!
Harry during the whole Felix Felicis scene is complete funny awesomeness. Harry, with his uncharacteristically peppy attitude, steals the entire scene (especially when he enacts how a giant spider's pincers work).
Seriously, Google "not to mention the pincers" on images. There's a bunch of them. And, it's hysterical.
The whole bit with Slughorn sneakily cutting a leaf from a plant in the greenhouse when Harry walking into frame in the background, turning and seeing him and getting right next to him without saying anything and Slughorn getting the crap scared out of him when he turns his head!
Right after taking the Potion, Harry's alarmingly happy "HI!" to a random dude.
There might be an interview somewhere, where Dan said that he enjoyed doing the Felix Felicis scenes because instead of acting like Harry, he simply had to act like himself.
Hermione: I think she's trying to smuggle you a Love Potion. Harry: Really? (smiles at her) Hermione: She's only interested in you because she thinks you're The Chosen One! Harry: But IamThe Chosen One. (Hermione slaps Harry upside the head) Harry: Sorry. Don't worry, I'll take someone I like. Someone cool. (hard cut to Luna)
Ron under the love potion. All of it. Ron staring at the moon when he was under Romilda Vane's love charm:
Ron: It's beautiful, isn't it? The moon. Harry: Divine. Had ourselves a little late night snack, did we? Ron: It was on your bed, the box, I just thought I'd try one. Harry: Or twenty. Ron: I can't stop thinking about her, Harry. Harry: Honestly, you know, I reckon she was starting to annoy you. Ron: She could never annoy me. I think I love her. Harry: Oh... brilliant. Ron: Do you think she knows I exist? Harry: Well, I'd bloody well hope so, she's been snogging you for three months. Ron: Snogging? Who are you talking about? Harry: Who are you talking about? Ron: Romilda, of course. Romilda Vane. Harry: Okay, very funny. Ron:(throws the chocolates box at Harry) Harry: What was that for? Ron: It's no joke! I'm in love with her! Harry: Alright, fine, you're in love with her! Have you ever actually met her? Ron: No... Can you introduce me?
One of these lines is said by Ginny, which (given her previous experiences) makes it borderline Black Comedy.
Then there's McGonagall's exasperated "Why is it always you three?" upon discovering Harry, Ron, and Hermione are caught up in the crisis du jour yet again. And Ron's reply, for that matter.
McGonagall:(to Harry, Ron, and Hermione) Why is it that, whenever anything happens, it's always you three? Ron: I've been wondering that myself for six years, Professor.
Price negotiations with Fred and George.
Ron: How much are these? Fred and George: Five galleons. Ron: How much for me? Fred and George: Five galleons. Ron: I'm your brother. (beat) Fred and George:Ten galleons.
Also, Fred and George each have different expressions when they say that last line, both funny.
Weasleys' Wizard Wheezes shop features an animated doll of Umbridge skating across a tightrope, squealing "I will have order! I will have order!" Let us hope there was a spiked pit under it and the doll was incinerated if you tipped it in.
When Harry and Dumbledore are about to leave for the cave:
Harry: But sir, I thought you couldn't Apparate in Hogwarts. Dumbledore: Well, being me definitely has its advantages.
On a meta level, from Slate.com's review of Half-Blood Prince:
The scene where Ron is in the hospital wing after being poisoned, and his annoying girlfriend Lavender comes in worried and asking "Where's my Won-Won?" She and Hermione get into a fight over him, where Hermione calls her a "daft dimbo"! What makes this even funnier is that it's happening in front of the teachers — Dumbledore, McGonagall, Slughorn, and Snape. Then Ron calls out Hermione's name in his sleep, and Lavender runs off crying; Dumbledore quips "Oh to be young and to feel love's keen sting!"
Dumbledore delivers that last line in the most airy, cheerful manner possible, like he didn't just witness an angsty teenage romance drama... or like he's seen similar scenes so many times during his years at Hogwarts that he's no longer fazed by them.
Don't forget that while McGonagall and Snape keep their cool after Lavender storms off, Dumbledore is the only one who turns to look at her.
Also the way that Snape just stares straight ahead during that scene. And the fact that he's there at all watching it. It also becomes a little funny and sad once you realize that he should know how Lavender feels...
When Dumbledore mentions Harry's quick thinking using the Bezoar to counteract the poison, Snape shoots Harry a highly surprised look, clearly seeming to wonder, "Did Potter actually remember somethingI taught him?"
And Snape probably knew (either through Legilimency or just because he's Snape) that Luna was Harry's date - and, more than likely, he was absolutely right.
A rather subtle one, but Slughorn's face sports a quick "Oh Crap" look when he accidentally rips off Aragog's pincer while trying to extract some of his venom? Right in front of a sobbing Hagrid, by the way.
After Harry and Ginny's first kiss in the Room of Requirement, Ron's line in the very next scene;