Hugo Strange is barely known outside of the comics world, but he's one of Batman's first villains, appearing just before both The Joker and Catwoman. He's been written as a mad scientist, Victor Frankenstein-style, and as a regular doctor who just happens to be an evil genius. Wikipedia has more.
Pros: Both Batman Begins and The Dark Knight focus Batman's attention on organized crime, and his interaction with the villains comes as a result of his pursuit of the mob, and the story I most associate with Strange (see below) can tie in nicely with what has come before. Also, this choice would earn major fanboy props for going with a villain most of the audience had never heard of. And getting character drama out of a psychiatrist seems pretty easy.
Cons: Fanboy props aren't worth much, since the trailer could show Christian Bale and Christopher Nolan holding giant bags of money and saying "thanks for making us rich, come see the third one and make us richer!" and everyone who knows who Hugo Strange is would still be there opening weekend. Many in the general audience still only know Batman from the Adam West series and the Tim Burton/Joel Schumacher movies, and using a villain those fans know is good for business. With Batman Begins, the creative team already showed a willingness to go with the obscure bad guys, but there might be pressure to stick with the better known foes after the success of The Dark Knight.
How I'd do it: A mad scientist doesn't fit too well in the film franchise universe, which is extremely realistic compared to most superhero movies, so the evil genius doctor it is. The best known Hugo Strange story (or at least best known to me) is from Strange Apparitions, in which Bruce Wayne visits a hospital run by Strange. Using his bag of evil genius tricks, Strange learns that Bruce Wayne is Batman, and decides to auction Batman's identity off to the highest bidder. This is, as I mentioned above, a perfect opportunity to have Gotham's gangsters bid on the secret. Or just try to beat it out of him.
Casting Guesses: I can't just pick one here, so here are three who would play the character very differently, I'm sure, but all would be great: Ben Kingsley, Paul Giamatti, and Zeljko Ivanek. Kingsley looks the part probably better than anyone. But Giamatti's such a fantastic actor that I know he'd do something unique and interesting. And Zeljko Ivanek has made a career out of playing seedy characters (and he was fantastic in Damages) which would be perfect for Hugo Strange.
Verdict: Hugo Strange wouldn't be my first choice, but I wouldn't have a problem with him either.
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.