Riddler is the villain in the Batman universe that obsessed with riddles, puzzles, and word games.
Riddler Papercraft

Professor Hugo Strange is a fictional character, a comic book supervillain in the DC Comics universe. He first appeared in Detective Comics #36 (February 1940) and is one of the first recurring villains Batman ever faced-wiki This is available until Dec. 31 only!
Dr. Hugo Strange Papercraft

The original Clayface, Basil Karlo, appeared in Detective Comics #40. An actor donning the mask of the villain in the movie "The Terror", Clayface, he embarks on a murder spree among the cast and crew of the remake. Available until the end of the year only!
Golden Age Clayface Papercraft

The Scarecrow (Dr. Jonathan Crane) is a comic book character that first appeared in World's Finest Comics #3 (Fall 1941). He was a former psychiatrist who uses a variety of drugs and psychological tactics to exploit the fears and phobias of his adversaries, the Scarecrow is a member of Batman's rogues gallery.
Golden Age Scarecrow Papercraft

This os one of the two holiday models from Professor Plastik. Two-Face is a comic book supervillain who was once Harvey Dent, a District Attorney of Gotham City and an ally of Batman. He becomes insane and turns into the crime boss Two-Face after the left half of his face is disfigured; he chooses to bring about good or evil based upon the outcome of a coin flip.
Golden Age Two Face Papercraft

Joker is one of the best known comic book villain and is Batman's main enemy. After his theft attempt was foiled by Batman, he fell into a vat of chemical waste and emerged with bleached white skin, red lips, green hair and a permanent grin.
Golden Age Villains: Joker Papercraft

You can probably recognize this bald guy. It's Lex Luthor, the arch-nemesis of Superman.
Golden Age Villains: Lex Luther Papercraft

Paperinside has started a park villains series with Joker as the first model.

Joker Papercraft