Talking about Hades, when the heroes finally confront him, he is hilariously pissed that people would think he was the one behind the theft. Percy suggests he would want a new war to get more subjects... and Hades angrily replies that, with all the people dying everyday (especially with the WWI, WWII, Korean War, Persian Gulf War, the War on Terror), he already has more subjects than he would want to or could possibly finance and organize.
"Do you have any idea how many new subdivisions I had to set up just in the twentieth century?"
In hindsight, his similar complaints about his Underworld expenses. His Roman form is Pluto, who lords over all riches underneath the earth (though Hades in this book claims ownership of all the gems and precious metals too) - apparently he can't help himself too well.
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:(says hello to the poodle).
Poseidon's summation of his brother after Zeus threatens to kill Percy if he ever dares set foot in his domain (i.e., travels by airplane or anything similar) and Zeus... flashy exit: "He would be an exceptional god of theatre."
Earlier, when Percy just arrives with the master bolt but hasn't taken it out yet...
Zeus: I should have shot you down with a lightning while you were on the plane!
Poseidon: And risk destroying your master bolt? Do think of what you're saying, brother.
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 Zeus, which is that any wine he tries to drink turns to water.
Dionysus: You know, the Christians have a guy who can do this trick in reverse. *beat* Now that's a god.
The best part is that he looks up when he says the last bit, as if making absolutely sure that Zeus can hear him.
Hermes mentioning the TV show Heracles Busts Heads. Made even funnier in the movie because Nathan Fillion plays Hermes, and he mentions that the show was 'cancelled before its time.'
The Titan's Curse:
Mr. Paul Blowfish, anyone?
Turns up later when Poseidon, entirely serene, thinks that it's actually his name. When Paul slightly testily corrects him, Poseidon says, slightly absently, "Pity, I quite like blowfish."
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 normally drives as a sports car, but 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 bus 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 constantly correcting 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."
Percy wondering how Kronos fits in to the disappearance of Artemis:
Percy's narration: "Kronos could influence people with dreams and trick them, but I didn't see how he could physically overcome Artemis if he was still like a pile of evil bark mulch."
The General's first attempt to grow an army of soldiers with dragon teeth. His minion confuses the teeth with sabercat teeth, which ends up growing adorable kitties. The General is not amused. Made even better by the fact that this is after he delivers an evil speech about his most invincible army, right before the kitties appear. One of these cats reappears in The House Of Hades.
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?
Percy's annoyance that the Olympians' Big Screwed-Up Family shtick is once again giving him trouble, this time in the form of slowing him down when he's on the clock.
Percy: If you're gonna kill me, could you, like...get on with it?
Demeter:Well. This one does have an attitude.
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.
Moments later, Percy notes his admiration of an Ares camper's ability to viciously cuss out a Hermes camper in perfect rhyme.
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's line about his powers of summoning the dead.
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 the Hellhound. 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.
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.