(Sorry for the bad english!)
1. He leaves impact on his actors.
Near the end of the filming of The Dark Knight, in which he played the Joker, Heath Ledger killed himself. Some say that he killed himself because of his role as the Joker left such an impact on him.
In the upcoming movie Suicide Squad, Jared Leto plays the Joker. While filming, Leto send to Margot Robbie (Harley Quinn) a live rat as a joke to show her how "method" he is. Although Leto probably just want to be awsome, some people think he has the "Joker syndrome".
2. The killing joke.
In 1988, english author Allan moore wrote a story so good, some believe it to be the best Batman story ever! SPOILERS!!! This graphic novel shows us the sick psychology of the joker and for the first time his origin. In this brutal story the joker and his henchmen shoots Barbara Gordon (Batgirl and the daughter of commissioner Gordon) in her legs, paralize her, and takes naked picrures of her. Then the joker kidnap her father, put him naked in a "tunnel of love" inside an abandon park and while he sees the pictures of his naked daugher, the joker's hencmen beat him. Lucky for Gordon, Batman came with the police for the Joker.
3. He killed Robin.
In this story, Jason Todd, the second Robin, tries to find his mother, but when he finds her, he find himself brutaly beaten by the joker, then the joker put a time bomb in the room which blow the whole place and killing Jason and his mother.
But dont worry, it's comics, and after 15 years he came back from the dead and became "The Red Hood".
4. He refused to work with the Red Skull because Skull is a Nazi.
In 1996, comics writer John Byrne created a crossover called "Batman and Captain America". in the comic book the Joker and the Red Skull worked togather to kill batman & robin and Cap & Bucky. But when the Joker finds out that Skull is a Nazy he says: "I may be a criminal lunatic, but i'm an AMERICAN criminal lunatic!" and they both start fighting.
5. Batman is actually afraid of him
In the story: "Death Of The Family" by Scott Snyder the joker threaten to kill all the Bat family. In the story Batman think about how he is always sceard when he hears the joke's voice. He trying to calm himself by telling himself that the joker is just a men, not some kind of monster. A men with eyes he never saw before