Harriet Cooper is Dick Grayson's Aunt, who comes to live at Wayne Manor after the death of Alfred Pennyworth. She was a recurring character on the Adam West TV show, and though many believe she was created specifically for that series, she appeared in the comic books well before the television adaptation.
Fredric Wertham's 1954 book Seduction of the Innocent claimed that comic books were an evil influence on young children, and specifically pointed to Batman and Robin as promoting a homosexual lifestyle. In an effort to address those concerns, writers killed off Alfred so they could add a female presence at home for Bruce and Dick.
Eventually Alfred came back to life, and Aunt Harriet left without too much explanation, slowly fading from memory. When DC comics rebooted their continuity in the 1980s, Aunt Harriet was eliminated, since she didn't fit with the grim and gritty style of Batman established by Batman: Year One.
Pros: With Rachel gone, Batman really does need a female presence.
Cons: You can't have Aunt Harriet without Dick Grayson. Also, she's a pretty uninteresting character.
How I'd do it: I wouldn't.
Casting Guesses: I dunno, Carol Burnett? She vaguely reminds me of the TV Aunt Harriet while still being great. But she would stick out like a sore thumb in a Christopher Nolan Batman movie.
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.