When his math teacher threatens him with a lot of pain in Book 1, 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!"
In book 2, when a male cyclops becomes engaged to Grover, who's playing along as a girl. Voice and all. 'Nuff said.
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.
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."
In the first book when Percy yells at the Minotaur: "Hey! ...Hey, stupid! Ground beef!"
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'..."
In Labyrinth, Annabeth happens to know the old trick of keeping to the left hand wall. She makes the mistake of saying so out loud, and the Labyrinth promptly changes to a circular room with eight identical doors.
Tyson: Left walls are mean.
Also happening with Annabeth in that same room, when she gets ticked off by Hera's 'help', and all the remaining food disappears before Tyson can finish.
Annabeth:[stamps foot in frustration] What sort of help was that?! "Here, have a sandwich. Make a wish. Oops! I can't help you! Poof!"
The scene at Hoover Dam in The Titan's Curse would fit here. 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."
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.
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.
At the end of the fifth book 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?
The scene in book one 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.
Sally's letter to Percy at the end of The Lightning Thief.
Mr. Blowfish, anyone?
The last conversation Percy has with his father:
Poseidon: You're doing well with those new cabins by the way. I suppose this means I can claim all those other sons and daughters of mine and send you some siblings next summer.
Percy: Ha-ha. (beat)
Percy: Um, you were kidding, right?
He never did give Percy an answer. :)
Dionysus has a rivalry with Blinky, the red ghost from Pac-Man. And he will have his soul, fictional character or not!
Tyson's Battle Cry from book five was pretty sweet...
Tyson: "PEANUT BUTTER!!!"
In Book Five, Percy sees visions of his loved ones while bathing in the River Styx.
Sally: "Percy. I give you my blessing."
Tyson: "Be safe, brother!"
This becomes even funnier when Percy lampshades it.
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.
"Can I kill him just a little bit?"
Kronos's Deadpan Snarker moment in book 5: "She forgot. Yes, that must've been it. Oh dear, I forgot my friend is invulnerable and took a knife for him. Oops."
In The Last Olympian, 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.
From the Demigod Files: Bob the Titan.
From The Sea of Monsters:
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?
Even if it was during a really tense moment, Hermes scratching his back with his caduceus and George and Martha (the snakes wrapped around it) going "Ow, ow, ow" was still worth a chuckle.
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.
The name of Geryon's ranch: Triple G Ranch (GGG Ranch). I thought it had a subtle shoutout to Hoodwinked, as Granny Puckett's nickname is "Triple G". Definitely no relation between the two.
Mrs. O'Leary ending up in Sally's Upper East Side apartment. No room for here. When Blofis pets her, there is a loud "BOOM BOOM BOOM," which according Percy means that either a SWAT team is breaking down the door or Mrs. O'Leary is wagging her tail.