You might be a bumbling oaf who's never leapt around precarious platforms using a grappling hook, but Batman ain't. To that end, you're unlikely to die from falling off a ledge in
Batman: Arkham Asylum - much as it was impossible to meet your demise from a slip of the foot in
Prince of Persia.
MTV Multiplayer's Russ Frushtick reveals that, should you get a bit clumsy, the game will slow down and prompt you to fire your grappling hook. Said hook will then whisk you away to the safety of the ledge you were just on, meaning you won't meet an embarrassing end unbefitting of the Dark Knight.
That's not to say, however, that enemies can't beat you to death. There's still every chance that you'll be pummelled into the grave beneath Killer Croc's leathery fists.