Obsessive compulsive who feels compelled to leave riddles forewarning of his future crimes. Also places victims in death-traps, with puzzles their only form of escape.
As Found in Wikipedia:
The Riddler is obsessed with riddles, puzzles, and word games. He delights in forewarning both Batman and the police of his capers by sending them complex clues. With this self-conscious use of a gimmick, the Riddler's crimes are flamboyant and ostentatious. The character is often depicted as wearing a domino mask either with a green suit and bowler hat, or a green jumpsuit. A black or purple question mark serves as his visual motif. Since the animated series and the film Batman Forever, Riddler often carries a trick "question mark" cane.
The Riddler is typically portrayed as a smooth-talking, yet quirky, victim of an intense obsessive compulsion. This was first introduced in the 1965 issue of Batman (titled, "The Remarkable Ruse of The Riddler") in which he tries to refrain from leaving a riddle, but fails. This compulsion has been a recurring theme, as shown in a 1999 issue of Gotham Adventures, in which he tried to commit a crime without leaving a riddle, but fails: "You don't understand. .. I really didn't want to leave you any clues. I really planned never to go back to Arkham Asylum. But I left you a clue anyway. So I... I have to go back there. Because I might need help. I... I might actually be crazy."
The Riddler was popularized by Frank Gorshin’s over the top, Emmy-nominated portrayal in the 1960s Batman television series. Jim Carrey played the Riddler in the 1995 film Batman Forever with Gorshin as his inspiration. The character was also featured in Batman: The Animated Series and The Batman, where in the former, he was portrayed as a smooth-talking intellectual who presented genuinely challenging riddles; in the latter, he is a much more sinister character with a Marilyn Manson-inspired design based on the traditional costume.
Unlike most of the other prominent members of Batman's rogues gallery, the Riddler is not a psychopathic murderer; a large portion of Riddler's crimes are non-violent in nature. Batman's direct conflicts with the Riddler are typically more cerebral than physical and usually involve defeating him non-violently.