A character for whom every thing is funny, and everything is worth a laugh. They see the funny side of everything, and you can expect this character to laugh regardless of whether he just got hit with a pie or missiles are raining down from above. They'll laugh through sun, rain, sleet and snow, and they usually do it so much that it becomes a sort of Catch Phrase for them.
For villains, this often overlaps with an Evil Laugh, and, in fact, this trope is more common for villains rather than heroes or neutral characters, and this often crosses with Comedic Sociopathy. It's also common for crazy people.
A good Boisterous Bruiser does a lot of laughing, just because they LIVE LARGE!
Do not confuse with LenaHyena. Compare The Pollyanna, who is always happy.
Incidentally, the inspiration for this trope, spotted hyenas (Crocuta crocuta), aren't really laughing when they make their infamous vocalizations. It appears to be a form of communication used mostly when fighting for food or in social conflict.
Hamburg, the Dumb Muscle of the Foxy Pirates, laughs at literally everything that happens around him. While, admittedly, some of these things are actually funny (like how a giant crewmate of his can never hear what anyone else says because he's so tall), he does it at every turn.
Miss Valentine, who appears for a whole story arc as a main villain, but only has three or four lines that aren't laughter.
While not prone to laughter as per the trope, Bellamy has "the Hyena" as his Badass Nickname.
Not to mention Bellamy's boss, Donquixote Doflamingo. Dude never stops laughing smugly.
Kururu from Keroro Gunsou utters his famous "ku ku ku" laugh, even when everything is going to hell around him. It seems like his standard reaction to everything.
Haruhi Suzumiya: Tsuruya tends to burst into loud laughter at everything she finds even slightly humorous. Her first appearance in the show has her utterly fail to stay in character while making Haruhi's student film because she's laughing too hard. She spends the rest of the scene laughing hysterically while Kyon does snarky narration.
Waji in Haré+Guu, has a rather creepy hyena like laugh. Apparently he believes laughing makes your worries go away. He was even compared to a hyena once. Interestingly there are a few hints he has a troubled home life, like being found in the middle of the night in the jungle, crying to himself.
Elmer from Baccano is always laughing or at least smiling, and spends his long life trying to make everyone else smile. He does this even when this would be completely inappropriate, such as just after the person has gone through a traumatic event, making it seem like there's something seriously wrong with him.
Sakamoto from Gintama. He wasn't always like that though.
Patti from Soul Eater. The Sun is also usually depicted as laughing.
In The Dark Knight, Batman threw him off a building and he laughed hysterically on the way down.
He also does this in the comics, in the arc "Lovers and Madmen", only rather than being thrown, he delibrately steps off, just to see if Batman will save him, despite having just gone on his very first rampage through Gotham City. This being, at the time, the official first encounter between the Joker and Batman, he survives, obviously. Not sure whether this example, or the Dark Knight, came first.
During the Amalgam Comics crossover event for Marvel and DC, the Darkclaw, a hybrid of Batman and Wolverine, fought a cross between Sabretooh and the Joker — named the Hyena, of course. Basically, a shirtless Joker on 'roids and a healing factor, topped off by a mane of green hair.
One story in an American-made comic set in feudal Japan featured a samurai, the principal courier for "the Great Lord", whose ability to see the humor in just about anything had caused him to be known as Harada the Jokester. Given a message to carry that would've forced the death of the two main characters, to whom he'd taken a liking, he picked a fight with a band of assassins, so they'd kill him before he could pass on the message. As the assassins closed in on him, he was laughing loudly.
This was the trademark of "Laffy" Smith, one of the villains in the Dick Tracy strip.
Have we ever discussed Socrates' laughter? He starts out laughing at whatever it was that amused him. Then he keeps laughing. It goes on and on, until finally he's just laughing at the fact that he's still laughing. The laughter stops whenever he passes out, or finally decides to calm down and try to catch his breath.
Films — Animation
Ed from The Lion King, who is a literal Hyena, and whose entire dialogue consists of insane laughter, which only his partners are able to understand. The others laugh pretty often too. Goes straight into horror when the other hyenas ask him about his opinion of Scar calling them "friends" shortly after denouncing them to Simba, and his only reaction is to laugh and lick his lips just before they all maul and devour Scar; not the loud cackle, but a quieter snicker.
The weasels in Who Framed Roger Rabbit?. Results in their demise. Judge Doom mentions that the weasels had some "idiot hyena cousins".
The Ghost of Christmas Present in A Christmas Carol 2009. His constant laughter quickly moves from jolly to unsettling and becomes downright scary as he continues to guffaw as his body ages into a skeleton and then crumbles to dust.
Johnny laughs at all kinds of unfunny things in The Room. One particular example is a scene where Mark tells a story about a girl who ended up in hospital. It's fucking weird. What he says is "What a story", implying the story might sound far-fetched to him.
Joe Cox, the African gang member from Robocop, laughed at everything, especially when people got hurt.
The Great Race: Prince Hoepnick (Jack Lemmon) is a cheerful fellow, loving the life he's living, constantly drunk, and punctuates nearly every sentence he says with a loud braying laugh. Ha HAAA Hhahaaa!
There's one infamous video from the early days of America's Funniest Home Videos of a man just busting a gut the entire clip and no one knows what he was laughing at!
Harvey Kneeslapper from Sesame Street. The character was eventually dropped because the laugh was destroying Frank Oz's voice. Averted on at least one occasion, when one of his practical jokes backfired on him; his would-be victim ended up laughing at him, and he naturally failed to see the humor.
Tim Curry's portrayal of Long John Silver in Muppet Treasure Island is a creepy hyena. At first, his laughs seem to just be the jovial nature of a simple ship's cook. As his true colors start to shine through, it starts to feel more and more menacing each time he starts.
The Teletubbies always laugh. They laugh because of their toys. Even the sun laughs.
With respect to the Teletubbies, Tilly, Tom, and Tiny from Tots TV and Rosie And Jim also made by the same company also seem to laugh a lot.
Bob And Ray had a recurring character known as "Charles the Poet", who would start out by reading a piece of awful poetry with dead seriousness, but within a few lines would completely lose his composure and break out into helpless laughter. This would get him yanked from the air well before he could get through to the end of the poem.
Exalted gives us Adorjan, the Silent Wind, a Yozi who, when she speaks, only does so through laughter. This is partially because of a Charm she has (and her chosen can learn) which allows telepathic communication while forbidding the bearer from vocalizing anything other than laughter, and partially for otherreasons.
In Shakespeare's A Midsummer Night's Dream, some interpretations Puck can certainly be described as such. Particularly in the 1930 version, where he was portrayed by a teenage Mickey Rooney.
Persona 4's Yukiko Amagi regularly has laughing fits that can last for several minutes. The one exception: even she doesn't laugh at Teddie's jokes. (The funny-nose glasses, though, leave her helpless.)
Father Grigori from Half-Life 2, who's on your side but nevertheless clearly has a screw loose. Escalated further in Concerned, where he laughs about once per speech bubble.
In the town of Wimbich in Zelda's Adventure, there's a guy in a shop who seems to think that everything up to and including "lighting a shrine" is a laugh riot (6:15 through 7:30 of this Let's Play video).
Hazama of BlazBlue is a complete axe-fucking-crazy version of this.
Reika Kirishima from Time Gal. No matter how dangerous the situation, she always finds something to laugh at. However, she does stop laughing when things get too dangerous. This only holds true for the Japanese version, however, as she's a lot less giggly in the US version.
Warp from Toonstruck never stops laughing, even after one of his pranks backfires and blows his head off he still laughs.
Homestuck: Terezi Pyrope, befitting the only troll who's actually any good at trolling. She loves annoying everyone just a little too much. Her sprite is also always drawn with an open mouth, showing off the fact that trolls have many more teeth than humans. Similarly, her lusus proves to be a much more lighthearted one when it's reincarnated as the Dragonsprite.
As mentioned above, the Joker, but special mention has to go to his protege in Batman Beyond, Little JJ a.k.a. Robin, who kills the Joker while laughing, only to break down into tears after he realizes what he's done.
Uhuhuhuhuhuhuhuh, Beavis And Butthead like, never stop laughing, ever, uhuhuhuhuhuhuh. It's, like, a Verbal Tic or something, uhuhuhuhuh. So much that on those rare occasions when they do stop laughing, it's either because something has just ticked them off or they're confused (well, more confused than they usually are). Taken Up to Eleven when Butt-Head is given laughing gas by the orthodontist because he won't stop squirming.
In an episode of Rocko's Modern Life, a satellite crashes into the kitchen, a state-licensed contractor (an actual hyena) comes in to look at the damage. He immediately cracks up and proves to be of no help to Rocko.