When his math teacher threatens him with a lot of pain, Percy thinks they figured out he cheated on his Tom Sawyer book project and might take away the grade. Or worse, make him actually read the book.
Mrs. Dodds's last threat: "Die, honey!"
"I wasn't sure where the Latin came from, but I'm pretty sure it meant 'eat my pants'."
Percy:Braccas meas vescimini!
Percy yells at the Minotaur: "Hey! ...Hey, stupid! Ground beef!"
Percy deliberately ticking off the gods by mailing Medusa's head to Mount Olympus in The Lightning Thief. The "With Best Wishes, Percy Jackon" bit is what really sells it.
Grover: They're not going to like that. They'll think you're impertinent. [After inserting a few drachmas into the package, it promptly disappears with a pop]
Percy: I am impertinent.
Percy "tearfully" rewarding the people of Los Angeles with free appliances from Smelly Gabe's store at the end of book one. He even provided the telephone number.
The scene where Grover tells Percy that he met a pink poodle named Gladiola who ran away and is willing to let Percy and the gang take him home for a $200 reward. And then they tell Percy to say hello to it.
Percy: I'm not saying hello to a pink poodle, forget it.
Annabeth:Percy, I said hello to the poodle. You say hello to the poodle.
Percy's narration: This was so completely unfair that I told Tantalus to go chase a donut, which didn't help his mood.
when a male cyclops becomes engaged to Grover, who's playing along as a girl. Voice and all. 'Nuff said.
Annabeth cut the rope [bridge], and the Cyclops howled...with glee, because he was standing right next to us.
After Percy and the gang battle a bunch of giant cannibals: "Can someone tell me what those were?" "Laistrygonians." "In English?" "Canadians."
The Canadian thing also shows up in The Heroes of Olympus, where it's revealed that Laistrygonian Giants really are Canadian - they show up in Vancouver to attack Frank Zhang's house. And then Percy calls them "Canadians", much to the offence of genuine-Canadian Frank standing right there.
After Percy and Annabeth narrowly survive being eaten by the sirens, Annabeth shares what she learned:
Annabeth: My fatal flaw. That's what the Sirens showed me. My fatal flaw is hubris.
Percy: That brown stuff they spread on veggie sandwiches?
Annabeth: No, seaweed brain. That's hummus. Hubris is worse.
Percy: What could be worse than hummus?
In the film version, Dionysus has this to say about the curse he got for ticking off Zeusnote Any wine he tries to drink turns to water.:
Dinoysus: You know, the Christians have a guy who can do this trick in reverse. *beat* Now that's a god.
The Titan's Curse:
Mr. Blowfish, anyone?
Apollo after Thalia crashes his sun chariot. "Well! You were right, my dear. You had everything under control. Now, let's go see if we boiled anyone important, shall we?"
The entire scene is funny in itself. Thalia is trying to drive the Sun Chariot (which Apollo turned into a shuttle bus to fit everyone) across the sky to Camp Half-Blood while everyone else is yelling directions at her and telling her to slow down and loosen up. Could also count as a Crowning Moment Of Awesome considering she was able to drive a flying shuttle buss all the way from Maine to long island without completely trashing it.
Poor, poor Zoe... "Lord Apollo has been going through this haiku phase ever since he went to Japan. 'Tis not as bad as the time he visited Limerick. If I'd had to hear one more poem that started with 'There once was a goddess from Sparta'..."
Thalia's attempts to convert Zoe's thee-s and thou-s into you-s.
The scene at Hoover Dam. Especially since Zoe's lack of knowledge of modern English made her not even get the dam joke.
Zoe: "Let us find the dam snack bar. We should eat while we can."
At the end Percy and his friends are victorious, Olympus is saved, the Gods are doling out rewards, Tyson is promoted to be general of the Cyclopes, and is granted any weapon he desires, creating a Mundane Made Awesome moment.
Zeus: what kind of weapon would you like? A sword? An axe?
Kronos's Deadpan Snarker moment: "She forgot. Yes, that must've been it. Oh dear, I forgot my friend is invulnerable and took a knife for him. Oops."
The scene where Percy and Annabeth witness the Ares and Apollo cabins fighting over a chariot they seized in Philadelphia. They see an angry Ares camper run by cursing in rhyme! "Curse me, eh? I'll make you pay / I don't wanna rhyme all day!" Annabeth groans, complaining that it took a full week for the rhyming couplets to wear off the last time Apollo cursed a cabin.
Artemis bugging Hades into sending all the Hunters who died in battle to Elysium at the end
Artemis: All those Hunters who perished in my service will never be forgotten. They will achieve Elysium, I am sure.
She glared pointedly at Hades.
Artemis glared at him some more.
Hades:*grumbles* Okay. I'll streamline their application process.
Nico: With great power... Comes great need to take a nap.
The Party Ponies. They're basically a fraternity of hyper-active centaurs. "HAWAII OWNS YOUR FACES!", anyone?
Oh, and the arrow that's fited with a boxing glove. Almost like a Get Smart device.
George's running gag of always wanting a rat and his and Martha's bantering. And what their names are. He seems to be too preoccupied on that.
Mrs. O'Leary. That is all.
Anytime Percy is jealous of Luke (particularly of Annabeth's feelings for him), Percy usually has something snarky to say.
Some of Percy's inner monologues are just hilarious. For example, "If you've never been charged by an enthusiastic Cyclops wearing a flowered apron and rubber cleaning gloves, I'm telling you, it'll wake you up quick."
Almost every character in the series says something funny, even when they do not mean it. Even Kronos has his moments.
The table of contents in every book is guaranteed to give at least a few laughs ("A God Buys Us Cheeseburgers", anyone?)
The title chapters have added hilarity due to It Makes Sense in Context. "I Scoop Poop" and "Nico Buys Happy Meals For The Dead" from the fourth book come to mind.
"We Hail the Taxi of Eternal Torment!"
"I Become Supreme Lord of the Bathroom."
Most of the times a God shows up for a one-off scene, especially when they are referencing well known heroic fantasy tropes in a casual manner as if they are entirely the way the world should work. Aphrodite in particular springs to mind as being ridiculously funny, but Hermes has his moments also.