Let's start with the most famous of the remaining enemies. Selina Kyle, Gotham socialite, lives a secret life as a costumed thief with a feline fetish who is on occasion involved romantically with Batman. Beyond that, her character has varied a lot over the years, and as you can see (from the cover of Catwoman: Nine Lives of a Feline Fatale), her costume has changed just as much. She's been a straight villain, a thief with a conscience, a protector of Gotham's East End, and briefly some kind of hooker dominatrix in Year One. See wikipedia for more.
Pros: Nothing against Rachel Dawes, but Bruce Wayne could use a stronger woman in his life. And Catwoman is as strong as it gets in Gotham. Catwoman is sexy, can hold her own in a fight, share's the Bat's fetish for tight fitting clothing, and lots of fun secret identity games can be played with Selina/Bruce and Batman/Catwoman. And without some of the goofiness factor that plagues a lot of Batman's villains, Catwoman would fit perfectly in the Gotham City of the Nolan Batman series.
Cons: The Halle Berry Catwoman stinker is too fresh in people's memories, and would probably scare Warner Bros. off the idea. The character has also been heavily exposed to the non-comic book community, having been played by Ms. Berry, Michelle Pfeiffer, Julie Newmar, Eartha Kitt, and Lee Meriweather. Plus, David S. Goyer, who wrote Batman Begins and gets a story credit on The Dark Knight, said he doesn't want to go with a villain who's already been in a movie. That doesn't mean it can't happen, since Goyer doesn't necessarily have final say on the matter, but it's certainly unlikely.
How I'd do it: Current Captain America writer Ed Brubaker and New Frontier's Darwyn Cooke revamped Catwoman in 2001 and it's been a top quality title ever since. Brubaker stayed on as writer for several years before handing over the reins to Will Pfeifer, who's done some excellent work of his own. I'd draw from their interpretation of the character. The more practical costume (center, above, with neither tail, heels, nor hooker boots), the antihero/thief who clashes with Batman's more strict morality, the protector of Gotham's street kids, junkies, and working girls.
Casting Guesses: Angelina Jolie (the default femme fatale choice these days) and Kate Beckinsale (she's already rocked a black catsuit a couple times) are the first women who come to mind, but they might be too obvious. I would very much like to stare at Megan Fox for a couple hours, but I'm not sure she can actually act. Carla Gugino would've been perfect a few years ago, but I think she might be a little past the age where an audience can buy her going toe to toe with Batman. The real answer for casting would, I think, be a relative unknown, but if I had to pick someone, I'd go with Charlize Theron.
UPDATE #2: Angelina Jolie is the first big (and unconfirmed) rumor for Catwoman casting, but there are now more (also unconfirmed) rumors that Maggie Gyllenhaal's Rachel Dawes character will somehow become Catwoman in the next movie. I don't buy it, but there are details here
UPDATE #3: Anne Hathaway is playing Catwoman in The Dark Knight Rises. See this page for all about Catwoman.
Verdict: Catwoman could fit perfectly with these movies, but it's probably not going to happen.
Would Catwoman work? Can people get over the awful Halle Berry movie? Should the third movie feature the Frank Miller prostitute Catomwan? Is there a perfect casting choice I didn't think of? And who should I look at next? Let me know in the comments.
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.