The Journal of Justice has this in spades. Along with giving extra info and backstory on the champions for the interested (quite a few) there are a number of "joke" articles which are just meant to be amusing. Special mention for Annie doing advertisements for dental hygiene. Yes, thatAnnie.
The Journal of Justice had an article, viewable on the wiki here, about Blitzcrank creating a sort of dating service. The article was amusing, but the best part was the accompanying illustration in which Blitzcrank shows photos of successful (well, he might have a different definition of it, being a robot and all) pairings from his service - one was Rammus and a cactus.
For Thanksgiving 2010, the Forums organized a AYAM, or All Yordles All Mid, game day. At the start of the game all players must pay their respects for Urf the Manatee by dancing in front of his grave, then fight to the death in a 5 vs 5 match with no retreating allowed. Things get a little crazy.
The two blooper reel videos Riot made of their own Season One CG Cinematic. The first is worth a good giggle, with Groin Attacks and Epic Fail but the second is HILARIOUS, asking Fridge Logic questions like "what if the summoner controlling a champion is a klutz?", "aren't those minions Cho'Gath eats actually animated contructs?" and "just how dog-like is Nasus?"
The tale told in this newspost. To give a quick brief, Mundo had taken a bunch of other champions to a bar, and the waitress kept asking, of all people, Rammus if the table wanted more drinks. I think you can guess the rest here.
Some champions' jokes.
One of his meme-laden joke quotes:
POWER LANING! POWER FARMING! POWER GANKING! POWER KILLS! SO MANY KILLS! 400 KILLS!note A reference to the memetic POWERTHIRST! commercial.
Even funnier when you realize that, due to his insatiable thirst for power, Xerath literally had MORE ENERGY THAN HIS BODY HAD ROOM FOR! So he got rid of it.
Xerath even has ENERGY LEGS.
He's also made of lightning. REAL LIGHTNING!
His joke emote is hilarious, and his quote seals the deal.
While the joke itself is a rather lame pun, the animation in which he performs his joke with is him SWIMMING IN MID-AIR. It's as bizarre-looking as it sounds, especially considering Nautilus himself. One of the loading screen hints even says "He's weird like that" in reference to the animation.
Not to mention, the classic Shout-Out joke by Pantheon. It fits him so well, and yet it will still bring a grin to your face. The delivery fits so well that for the shout out line, Pantheon was all shouting and serious, but then goes very laid back, the Mood Whiplash is just grin-worthy.
Guardian Angel is an armor that revives you on the spot with roughly half your HP on death, playing the animation in reverse to simulate getting up. Kog'Maw's death animation involves him exploding, so it would be kind of weird on him if he should somehow equip it. Thus, Riot has the item coded to play his dance emote when its ability goes off instead.
Some of the champions' alternate skins are hysterical:
The dances in general will cause you bust a gut laughing. Some are expected, such as Olaf's dance being based on "Techno Viking" and Corki "Doing A Barrel Roll". Some, however, are completely out of left field, like Twisted Fate channeling his inner K-Pop star by dancing to "Gangnam Style"!
One better. Urgot, the undead cyborg monstrosity, does the Kirby Victory Dance!
What is probably the best one, however, doesn't even belong to a champion. Vilemaw, the boss for the Shadow Isles version of Twisted Treeline, is a gigantic undead spider. Dancing within a certain radius of him makes him do The Carlton Dance.
The trailer for the Mac version is also highly amusing. It starts with Corporate Mundo going where he pleases and ends with one of Zigg's hexplosives standing in for the Apple logo. It also includes such hilarities as a child's drawing of Mordekaiser standing next to a burning house with "I [heart] My Daddy" written on it, a banana included on a display wall together with a collection of other weapons, an emergency glass cabinet with "Press R to win" printed on it and a water cooler that dispenses health and mana potions.
Another hilarious fan video is a clever parody of Coolio's "Gangsta's Paradise"- ladies and gentlemen, may I present "Yordle's Paradise".
Even professional teams can have a good sense of humor. Case in point: Season 3 World Championships, Group B, Fnatic vs. Mineski. For the record, Team Mineski had lost every match during the group stage up to this point, while Team Fnatic had a score of 6-1. Team Mineski knew that they couldn't enter the quarterfinals while Fnatic were almost guaranteed to get there. So what does Team Mineski do? Create a four man support + 1 ADC team, where each lane plays a support. note This strategy falls into the Awesome, but Impractical category. This is something that hasn't been seen since season 1, since while a four support team with ADC grants strong utility and pushing power, they lack any form of damage. A lot of mages, bruisers, and assassins provide some form of crowd control while dealing a lot of damage at the same time While Mineski pushed the towers early, they lacked any form of damage, and eventually Fnatic won the match. However, the crowd cheered for Mineski and a fan following was created because despite losing, Mineski at least has some fun and had good team spirit while showing great sportsmanship playing in the world championship, a rare accomplishment from a Southeast Asian team (since most teams rarely manage to enter the world championship).
The Road to the Cup video trailer is trying so hard to be awesome that it's hilarious. Watching animated renditions of fairly normal-looking pro-gamers in T-shirts and pants leaping around doing martial arts kata and unleashing flashy special moves of their most-played characters is cool, but endearingly ridiculous.
The Korean text for 'Annie' also is the same text that begins 'Anivia' - as such, in the Korean tournament OGN Champions Winter 2013-2014, Anivia (a rare and not particularly strong pick) has been repeatedly banned instead of Annie (a fairly strong support), much to the chagrin of the teams that do it.
URF Mode, an April Fools' Joke, turned into one of the most popular game modes implemented. However, the Team Solomid vs. Cloud 9 Gaming exhibition was completely chaotic, awesome, and hilarious all at the same time.
The Rise of the Dragonslayer video has a subtle one. It was supposed to highlight the new Dragonslayer skins and slaying Dragons, be it neutral Dragons, or Shyvana. But in a blink-or-miss, Dragonslayer Pantheon still have time to lob his spear to a nearby Teemo even though he's not a Dragon!
Casters vs. Doom Bots of Doom. 38 minutes of unbridled hilarity, including casters taking the piss out of a few of the pro teams in the scene and having Poro plushies stand in as live audience (and doom Bot players, complete with audience cheering!) in the studio.