Ava's entire dialogue during the quest "Animal Magnetism".
In the 2012 Christmas event, when you give a stray dog a bath, "Monsieur Flea" shouts at you for "flooding his home with no warning" and swears that is not the last you've heard of him.
And sure enough, when you give one of the strays a home, you can get him a flea circus. Guess who's in it?
In "The Void Stares Back," while the player is busy controlling Void troops fighting Void Pest forces via magical communication orb a.k.a. Commorb (The player, and several NPCs, are stuck behind rocks), Lord Daquarius, the leader of the Black Knights, laboriously mines the rocks to create an escape passage (gaining a level while doing so). After defeating the Pests, Savant (The Commorb contact), teleports the group out, with Daquarius screaming "WHAT!?!?" right before the teleportation. Also, he was mining with a bronze pickaxe.
In "King of the Dwarves", you must get help from a troll warlord called Pretty Flower (trolls are named after the first thing they try to eat). Before he listens to what you have to say, you have to prove you are worthy. He tells you 'You must lift up Big Rock' so you go and lift the big rock near him, not an easy task. He says 'No, that not right! I tell you to lift up Big Rock!', and then the previously unnamed troll called Big Rock goes 'Me bet you not strong enough to lift me.'
Also, most monster/item names are changed to what they appear as to Thok. (Silver curvy thing for a silver crescent key, sea meat for fish, Pretty Lass for the Divine Skinweaver you save, and so forth.)
The ending to "Let Them Eat Pie", as well as the dialogue with a person who witnessed it, is too funny for words to describe. Let's just say it involves a pie.
There's one quest where you need to find a brain surgeon to fix a bunch of monks after their brains were swapped out for zombies (long story). After you find the doctor in question, get him to the monks, get the supplies, etc, etc, he finally starts the brain transplant. Before he starts, he asks your Player Character to record what he does, for posterity. The scene cuts away to a graphic of a cat playing with a ball of yarn. When the scene comes back...
Player Character: I DON'T WANT MY EYES ANYMORE! I think I'm going to vomit...
Dr. Fenkenstrain: If you do, do it in a bucket. This is a sterile environment after all.
Philipe snarking at the player for not testing the guards' patrol, saying that there's a glitch, and asking why he can't kill all the guards. These are probably take thats or shout outs to players complaining about glitches and not being able to kill everything. Also, when you hand the boy a dress as a disguise, he is told that his father wanted him to wear it, making him think that his parents wanted a daughter.
The "guard"'s reaction to this makes it even funnier.
Claus the Chef: Heavens preserve us, it's the kid. In a dress.
Philipe Carnillean: Brave guard, you must be weary from your long vigil. Pray take your rest and sup with me awhile.
Claus: Do what with you awhile?
Philipe: Just take the drink!
Claus: The drink! Finally! Give it here, kid. *Takes drink and falls unconscious.*
Philipe levels up (quite frequently, in fact) during his battle against the Cave Wolf Matriarch and gets a "Quest Complete" screen. Bottom of the rewards list? Some self-respect.
If you aren't incredibly frustrated by One Small Favour, you're probably laughing your ass off.
During the quest "Stolen Hearts", you need to sneak into Al-Kharid's palace through a series of roof-hopping parkour tricks reminiscent of Assassin's Creed, like climbing ladders in a showy fashion, hopping across support planks, and swinging across makeshift monkey bars. Eventually you come across an awning that you need to jump on, so that you can bounce up high and climb onto a platform some distance away. Examining the awning simply gives the one word description: "Really?"
In the sequel quest, you get to jump from a building into a cart of hay. Of course, Ozan wants to go again.
Later on, a sundial is missing a piece, and it turns out that Ozan was sitting on it.
Right before that, the two of you sink into quicksand, with Ozan lampshading that quicksand doesn't work the way this batch does, and that it's not real quicksand.
Also, the tunnel scene. Ozan steps in... something, grabs what he thinks is a torch but is actually part of the player, and keeps commenting on the smell and sounds in that area.
Likewise, the player keeps shushing Ozan when he tries to use a certain term for dung, and Ozan's reaction to it. The player's explanation for why they were shushing him doesn't make it any less funny.
In "Some Like it Cold", one of the escape plans mentioned involves creating a second iceberg and moving all of the seals onto it. Even Teddy the polar bear cannot decide whether it is madness or genius. Other plans involve activating the nonexistent fire alarm, lassoing an albatross with underwear to hitch a ride, lying on their backs to spell HELP(won't work since penguins have white bellies), and launching out of the blowholes of killer whales. Also, Megapenguin.
Bringing Home the Bacon. All of it. Special mention goes to the bit when you beat the hell out of a pickpocket and the scene cuts away to a pig and a kitten while the pickpocket screams in agony in the background
Pretty much all of the dialogue was funny in some way or another. Poor Holstein, trying to have a serious debate. In a podcast released before the event, some Jagex mods were reading player questions. One question asked if anything in the event would be serious. Cue laughter all around.
During Fate of the Gods you can leave Freneskae and check in with Azzanadra and Sliske at the World Gate and update them on your progress. They also engage in some humorous banter, however this one line Sliske says to Azzanadra is defintely a Funny Moment:
Sliske: Big Boss to Bunny Ears, Big Boss to Bunny Ears. Come in, Bunny Ears.
In the Player Owned Ports minigame, there's a newbie adventurer NPC that asks you for advice on several things. You're given a range of options that vary from excellent to terrible. Much of the bad advice, and even more of the terrible advice is hilarious by nature of being complete violations of common sense. A comprehensive list of all questions that she asks, and all possible answers can be found here. A few choice examples:
Meg: Okay, so a friend of mine told me he's heard rumours of a powerful flail that was wielded by one of Saradomin's generals way back in the God Wars. I'm going to go and quest for it. Do you have any suggestions on where to start?
Player: Keep buying flails until you get the right one.
Meg: I was trying to disarm someone at range, but it's tricky. What do I do?
Meg: I want to cross terrain faster. What animals are safe to ride?
Player: Fire elementals.
Meg: So, I was planning on making a canoe and sailing to some of the wilder places downriver. Tell me, what's the best wood to use?
Player: Bloodwood trees. You can get to those, right? note Bloodwood trees are only available in incredibly dangerous areas, the logs crumble into dust if carried more than a few steps away from the trees they were cut from, and can only be crafted into bolts.