Bane was introduced in the 1990s at the height of the comic collecting boom that turned comic book creators into millionaires and celebrities, and later almost ruined the industry. He was one of the central characters of the Batman story Knightfall which was wildly popular, but in hindsight disliked by many fans including me. Telling Bane's story involves some heavy Knightfall spoilers, so proceed with caution.
Born inside a prison in a corrupt Caribbean island nation, Bane is sentenced to serve a life sentence for a murder committed by his dead father. With nothing to do but train, fight, and read, he share's Batman's obsessive dedication to better himself. He's forced to participate in a trial of an experimental drug known as Venom which gives its user superhuman strength. Eventually he escapes the prison, bringing his Venom and for some reason a luchador mask with him, and he decides to test himself against the best man the world has to offer, Batman. Unusual for a Batman villain, he attacks patiently and tactically instead of flamboyantly. His strategy is to break every inmate out of Arkham Asylum, forcing Batman to work around the clock to bring in psychotic criminals like the Mad Hatter. Then, only after Batman has worn himself out, does Bane strike. And Bane whips Batman's ass. Badly. He breaks Batman's back, leaving Bruce Wayne paralyzed. And that's where the story goes off the rails, as far as I'm concerned. Eventually, he's defeated, obviously, and Wayne walks again.
Subsequent stories have gotten Bane off the Venom, robbing him of his superhuman strength, and ignored his formerly brilliant mind, taking away the only things that made him interesting. He briefly teamed up with Ra's al Ghul, had a thing for Talia, and at one point thought Thomas Wayne was his real biological father, but he's been turned into a mindless thug who reminds everyone that he's the man who "broke the Bat," but poses no real threat anymore, and only pops back up again to capitalize on his popularity from the Knightfall.
Pros: Knightfall, as I said, was hugely popular, and even though I only liked parts of Bane in it, he has many devoted fans. The idea of someone who can be a physical and mental match for Batman is nice, since most of his enemies are one or the other.
Cons: He's a big strong guy in a luchador mask. That works ok in comics, but picturing that guy walking around in the movie version of Gotham is... odd. He also appeared in Batman & Robin as Poison Ivy's muscle, though he didn't speak and aside from the name, the venom, and the luchador mask, had nothing to do with the comic book character. And as I mentioned in my thoughts on Poison Ivy, anybody from that movie is a hard sell because it was just dreadful.
How I'd do it: You can keep his origin unchanged, although it might be fun to have him grow up in the prison Bruce Wayne spent time in in Batman Begins, but you might have to ditch the luchador mask. And the venom won't work, though he can certainly be on all kinds of steroids. The Knightfall storyline can be heavily modified to work for where the story of Batman has to progress. Obviously, breaking Batman's back and leaving him paralyzed would be far too slow-moving a story for one movie. But Bane could come to Gotham, taking out Batman in exchange for control of the mafia. He doesn't kill Batman obviously, but he defeats him, very publicly, leaving Batman broken, physically and psychologically. Bruce decides to give it all up, that he's found an enemy he can't beat. The people of Gotham, still hating him for the events at the end of The Dark Knight, celebrate Batman's defeat, making Bruce's decision to quit even easier. But with Bane in control of crime in Gotham, things get worse than they ever were. The people of Gotham, and eventually Bruce as well, reconsider, and Batman comes back better than ever to defeat Bane and redeem himself to his city.
Casting Guesses: The Rock? He's charismatic and physically big enough, but I'm not sure he can play a cold, calculating villain. Vin Diesel is kinda short and can't act. Maybe there's some huge wrestler somewhere who's perfect for it, but I'm not a wrestling fan.
UPDATE: Tom Hardy will be playing Bane in The Dark Knight Rises. See this page to read all about Bane.
Verdict: It could happen, but I hope it doesn't. Everyone expects the next movie to focus on Batman's redemption, and the Knightfall-ish storyline above fits that idea well. That version is horribly predictable, and while professional writers could do a better job, I don't think they can deviate too much from it without turning Bane into something else entirely.
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.