People still ask, "If you had any superpower, which one would it be?" Meanwhile, the most successful superhero is a guy who has no powers. Actually, he does have a power, the most powerfull of all.
Batman's been around for over 70 years - he's been played in live-action by seven different actors, he's starred in a bunch of cartoons, had his face plastered all over merchandise, and supports a whole line of comics - a "Batman Family" of books - within DC's line, for over the last 20 years.
Some credit this success to the fact that he's a very flexible character - open to differnet interpretations, yet never inconsistant; no matter how light or dark the portrayal, he remains Batman. How is this possible? I suspect it has a lot to do with the fact that his origin came sometime after he was introduced, and when you're working backwards like that, it means you have a concept first, and when that happens, it's possible to go any which way you please, because the backstory came later. That's how you wind up with the giant props, the cheery sidekicks, magic creatures, crazy costumes, goofy adversaries - the whole bit. Strip away all these elements and you can still tell Batman stories. Add in more elements and you can still tell Batman stories. He's still The Dark Knight. And The Caped Crusader. And The Masked Manhunter. And The World's Greatest Detective.
There are disagreements as to which interpretation is considered proper Batman. Some think it's the recent movies directed by Christopher Nolan. Others believe it's the popular cartoons from the last two decades, which feature a fully-realized Batman that outclasses the one that appeared in comics simultaneously. Some say it's the Batman of the 1st Tim Burton film. Some people think it's the Saturday morning Batman that hanged out with Scooby Doo and the Superfriends.
And there are many that think Adam West is still the best Batman - event though that show has been written off as a spoof. Use of the word "spoof" seems recent to me - just a way to give it a place on the shelf. Personally, any time I've picked up a book reprinting Batman comics from the 40's-60's, I've found the writing to be no different in execution than the show, save for a few knowing winks and nods to the audience. The same goes for the Superfriends - it may have been a spinoff of Scooby Doo, but the Justice League comics were not too different from the show, save for it being overrun with 2nd and 3rd string characters.
Why is it that one interpretation never stomps out the others? I recall Batman's light blue and grey costume lasted well into the mid-90's, and still appears in merchandise, and in a recent cartoon, 'Batman: The Brave and The Bold" which offers a light and fun Batman. Maybe the light and fun Batman seems more human than the Dark Knight. Maybe a lighter touch can endure the ridiculous merchandising demands and ebb and flow of audience tastes better than Mr. Serious. Is the Dark Knight fun for a dreary Sunday afternoon?
Regeneration is quite an amazing superpower - do you think he was bitten by a radioactive bat? That's a story that'll never be told.