Either from Superman comics, the Legion of Doom from Superfriends, or from Seinfeld, lots of people are familiar with Bizarro, the opposite version of Superman. But recently, Batman got his own version of the bizarro character, Batzarro. Batzarro does the same opposite talk as Bizarro, and wears both his utility belt and the bat logo on his chest upside down.
Pros: Batzarro's a fun idea, comics-wise.
Cons: It's a fun idea, but mostly a one note joke. It's too weird a concept for even a Fantastic Four movie.
How I'd do it: I don't think there's a way to turn an opposite Batman into a realistic-ish character that would remain in any way Batzarro.
Casting Guesses: Christian Bale in heavy makeup?
Verdict: Nope. Smallville had to go to great lengths to change Bizarro to get him to fit in their world, which is considerably wackier than the Superman movies, which are in turn considerably wackier than the Batman movies.
After The Scarecrow, Ra's Al Ghul, The Joker, and Two-Face, who should be Batman's next enemy in the Batman Begins/The Dark Knight series? Well, as of now we know that Tom Hardy will play Bane and Anne Hathaway will play Catwoman.
Check out the master list for all the villains covered. I've pretty much run out by now. Obviously, there are more Batman villains, but not any of significance that I know of. As of February 2009, no one is confirmed as a villain. Not the Johnny Depp Riddler, not Phillip Seymour Hoffman Penguin, nobody.