When people think of the word chaos it can invoke a lot of different things. On definition alone, something that is chaotic is completely disordered. Chaos takes on a different meaning in regard to a character's alignment. Used in most fantasy RPG games like D&D, a character's alignment is based on their morals and ethics.
A character who is chaotic, based on alignment, is a character that values freedom above most other things, and they don't like to work within any sort of established authority. Someone who is chaotic isn't necessarily an evil character, but they are categorized as being reckless and irresponsible, though they're also able to adapt to things quickly and aren't rigid in their thinking.
6 Juri - Chaotic Evil
Juri Han was first introduced in Super Street Fighter 4 and ever since her first appearance, she has been a prime example of a chaotic evil character. She's a ruthless and sadistic fighter who actually enjoys hurting her opponents. Her fighting drive comes from wanting revenge against M.Bison and she is willing to do anything to realize that desire of hers.
She's very hot-tempered and becomes angry when things don't go the way she wants them to. Despite all the evil things she has done and is capable of, Juri has fought alongside and even saved a few of the good characters. She despises M.Bison and Vega, and has helped out Cammy and Chun Li, though she still enjoys antagonizing the two women.
5 Travis Touchdown - Chaotic Good
Not all good or heroic type characters led righteous lives or are shining beacons of niceness. Sometimes they can be jerks, or they can act in ways that are against the status quo. But what sets a chaotic good character apart from a chaotic evil character is that they have good hearts deep down. They're just often very free-spirited. And Travis Touchdown can be put into that category. He's the protagonist of the No More Heroes series, though he's pretty crude and immature.
He's also an assassin and his reasoning for getting involved with the United Assassins Association and killing most of the top-ranked assassins is pretty selfish. Despite his superficial reasons for fighting, Travis has a moral code that he follows. He spares Shinobu, and he has honor and respect for those that he believes are "true warriors". And eventually, he vows to take down the UAA and avenge all the people that died because of them.
4 Rouge The Bat - Chaotic Neutral
Someone who is chaotic neutral is, most of the time, just out for themselves and their own interests. They don't really have any malicious intent to call them chaotic evil, but they don't always have everyone's best interest in mind. Rouge the Bat fits this category very well. As a thief with a particular interest in jewels, Rouge has set her sights on the Master Emerald and the Chaos Emeralds putting her at odds with the heroes, particularly Knuckles.
She will lie and manipulate others with her charm to get what she wants, but she's not without her own morales, and she has shown to be loyal to and care about others, particularly Shadow the Hedgehog in Sonic Adventure 2, Sonic Heroes and Sonic Battle.
3 The Joker - Chaotic Evil
The Joker probably embodies what it means to be truly chaotic. He's a homicidal super villain with a dark and twisted sense of humor. He has no loyalty or compassion for anyone and the terrible crimes that he commits are all done for his own amusement and ego. He is one of the main antagonists in the Batman Arkham series and all of his plans are meant to cause as much anarchy, destruction, and death as possible.
He is obsessed with Batman and has the desire to make him suffer and destroy Batman's spirit and beliefs. In the Arkham series he becomes the most notorious and dangerous super villain in Gotham, to the point that in his absence crime actually goes down by a lot.
2 Doom Slayer - Chaotic Good
Doom Slayer is the protagonist of the games in the Doom series. With a name like Doom Slayer (or Doom Guy), one who was not aware of what the games were about would think that he was evil. He isn't, though he is absolutely a prime example of a chaotic good character. He's the nightmare for all demons and shows no mercy to any demons that get in his way, but his rage and brutality don't extend to any humans.
His whole thing is saving humanity from the demons of Hell. The only time he's ever held ill will towards anything that wasn't a demon was during the first Doom as he assaulted a commanding officer that wanted him to fire into a crowd of unarmed civilians, and Samuel Hayden because of his plans to mine Hell for energy that cost many human lives.
1 Goose From Untitled Goose Game - Chaotic Neutral
The Untitled Goose Game made waves when it was first released as people deeply enjoyed playing as a troublemaking goose that terrorized a small English village. Players had to solve various puzzles by interacting with different things in the environment. Despite sometimes having to steal things and even chase a child into a phone booth, the goose didn't really have bad intentions, though it didn't have good ones either.
At most, the goose's actions were annoying and slightly hindered the people of the village from enjoying a normal day. That makes the goose from the Untitled Goose Game the perfect example of a chaotic neutral character.