It's impossible, I tell you, impossible! My trap was perfect! How did he do it!? I have to know! SOMEBODY TELL ME, IT'S NOT FAIR! There was no way, I tell you! NO WAY he could have gotten out! Somebody tell me! DO YOU HEAR ME!? SOMEBODY TELL ME HOW HE DID IT!! I HAVE TO KNOW!! I HAVE TO KNOOOOOWWW!!!!
~ Riddler goes mad after being outsmarted by Batman yet again
The Riddler (Real Name Edward Nygma) is a recurring villain in the DC Animated Universe cartoons, most prominently in Batman: The Animated Series (the cartoon he debuted in). Like other iterations of the character, he is an egotistical supervillain obsessed with outsmarting his opponents and with leaving riddles at the scenes of his crimes to confound his victims.
Edward Nygma was originally a simple software engineer with a love of puzzles, games, and riddles. He worked initially for Competitron, and created the game "Riddle of the Minotaur". Although the game was hugely successful, and many of Competitron's people became wealthy as a result, the Corporate Chair Daniel Mockridge responded with ingratitude, firing Nygma and casually dismissing his efforts as "insignificant", instead arguing that the company's success was owing to its skill with business negotiations and obtaining favorable contracts (i.e., to himself). To rub salt in the wound, he also revealed that Nygma's contract stated that he was not entitled to any royalties or copyrights of the game.
As the Riddler
In "If You're So Smart, Why Aren't You Rich?", outraged by his unfair treatment, Edward Nygma returns to Gotham City after two years as "The Riddler". He kidnaps Mockridge and planned to kill him, but also offers Batman the chance to save Mockridge provided he solved all of the challenges Riddler had laid out for him. The final challenge would be a run through the maze at the Riddle of the Minotaur amusement park, which was an actual simulation of the game Riddler had designed. Confident in his genius and assured of his victory, the Riddler was surprised when Batman successfully solved all of his riddles and outsmarted him. However, Riddler managed to escape Gotham City, also achieving his revenge on Mockridge in a manner more subtle than he had originally intended: Mockridge was traumatized by the whole near-death experience, seemingly scared of the Riddler's return for the rest of his life, yet it seems that the Riddler never returned to make him pay for his actions.
In "What Is Reality?", with Batman having figured out his identity, the Riddler takes extreme measures to protect himself; he goes on a campaign to eliminate all traces of his former self by breaking into banks and government buildings to destroy records bearing his name. He also sends a computer to the Gotham City Police Department with a virtual reality simulation that ends up trapping Commissioner Gordon. Batman enters the virtual reality world to rescue Gordon, and Riddler ends up destroying his dream world by focusing too hard on trying to kill Batman. Not only that, but the electronic backlash leaves his brain suspended, with Batman, Robin and Gordon finding his inert body at his hideout later in the abandoned Gotham's World Fair, helplessly leaving the Riddler behind with no way to know if he would ever recover.
In "Trial", having somehow recovered from his previous condition offscreen, the Riddler partakes in the trial of Batman held by various members of his Rogues Gallery, led by the Joker. He was not present for all of it though, meaning he might have taken the opportunity to escape in the chaos. In any case, he was most likely jailed again like all the other rogues after Batman and Janet Van Dorn manage to defeat the Joker and escape.
In "Riddler's Reform", the Riddler is revealed to have been released on the grounds that he'd been "reformed". Joining with Charles Baxter, one of Gotham's well-known toymakers, the Riddler invents several puzzles that quickly become popular with children, with Baxter having hired him in the first place because he wanted to use Nygma's Riddler persona to boost the company's profile. However, the Riddler secretly continues to commit daring robberies, leaving clues through his company advertisements. For his part, Batman is confident that Riddler will never be able to stay reformed and that he will inevitably return to crime. With this in mind, he confronts Riddler, and Riddler decides afterwards that, in order to truly have a fresh start, he needs to kill Batman. So to this end, he lures him into a booby-trapped warehouse and rigs the place to blow. However, Batman survives by simply concealing himself in a nearby safe, unknown to the Riddler, who was then arrested by the police after his crimes were exposed and returned to Arkham, ending his partnership with Baxter. With Batman refusing to tell Riddler how he survived, Riddler snaps completely and goes mad trying to fathom how Batman could have possibly outwitted him yet again, leaving his mental state worse than before.
Superman: The Animated Series
In "Knight Time", the Riddler makes a guest appearance alongside other members of Batman's rogues gallery. After Batman disappears thanks to Brainiac's machinations, the Riddler makes an alliance with the Mad Hatter and Bane to take over Gotham City. However, Robin and Superman disguised as Batman appear on the scene and Superman quickly defeats Bane while Robin handcuffs the Riddler on a cage and lifts him up, leaving the Riddler and Bane for pickup by the GCPD and taking the Mad Hatter with them so he can help them to find Bruce Wayne.
The New Batman Adventures
In "Over the Edge", following Batgirl's death at the hands of the Scarecrow and James Gordon's manhunt for Batman and his Bat-family, the Riddler along with the Ventriloquist and Scarface, Harley Quinn and the Mad Hatter fill a lawsuit against Bruce Wayne for his previous actions against them as the Dark Knight. However, as it turns out that most of the episode's events were only Barbara Gordon's fear gas-induced nightmares, nothing comes up.
In "Judgement Day", after The Judge stops The Penguin and Killer Croc, he goes to stop the Riddler from committing crime in Gotham City ever again. When the Riddler conducts a random heist in a restaurant, the Judge restrains him before doing the same to his henchmen. With no one to help him, the Riddler is left able to do nothing but look on in horror as the Judge drops an oversized book on him. It's presumed that the Riddler was either seriously crippled or killed as a result, as this is the last time we see him in the DCAU, so it's likely he never returned to crime afterwards.
Paul Dini, one of the main writers of Batman: The Animated Series, noted that Riddler was the hardest villain to write due to his being so cerebral in nature but also being obsessed with riddles, which Dini regarded as being close to self-parody; many Riddler scripts were rejected for being either too long or too silly. This would explain why Riddler had relatively few appearances in the DCAU.
In The New Batman Adventures, the Riddler wears a green jumpsuit and bowler hat to replace his previous outfit and domino mask, which he had destroyed in "Riddler's Reform". He also shaved his head to reflect his new outfit.
The Riddler was originally intended to return in Justice League Unlimited as a member of the Legion of Doom led by Lex Luthor and Gorilla Grodd as a nod to his inclusion in the original Super Friends season Challenge of the Super Friends, but such plans never materialized due the Bat-embargo. Had the Riddler appeared, however, it's likely he would have survived the Hall of Doom's destruction by Darkseid in the series finale, as the writers wanted to only have the thirteen original members of the Legion survive.