We watched a show on Animal Planet tonight that was all about this crazy bastard who free dives with all sorts of sharks, up to and including tigers and great whites. (That link will take you to a video of him doing just that.) Not that I have any desire to emulate the guy whatsoever, I have to say his cause is noble (he's all about getting people to stop killing sharks), and it's also pretty interesting what he's managed to do.
Apparently, many (most?) sharks succumb to something called Tonic Immobility under different sorts of stimuli. This catatonic trance is similar to "playing possum," though it's not clear exactly why it happens. It has at least something to do with how sharks mate; the males of some species bite the females and then flip them over on to their backs. Once inverted, the females go completely limp for something like 15 minutes on average. Fertilization happens, and the eggs have a chance to remain undisturbed for a decent amount of time before the female wakes up and swims away.
Various shark experts around the world have figured out how to induce "tonic" in the animals. The method depends upon the breed of shark. Very small sharks (e.g., juvenile lemon sharks) can be manually flipped on their backs, at which point they go immediately limp. Medium-sized, pointy-nosed reef sharks are sent into "tonic" by having the undersides of their noses stroked, where there are a multitude of nerve endings. Tiger sharks (which are really very pretty, by the way) are sensitive along the sides of their square noses, rather than the underside. And once they're out, they're really out. The scientists on the show were collecting blood samples and implanting subcutaneous radio tracking devices, and the sharks didn't even seem to notice.
Anyway, definitely give it a watch if you happen to come across it while channel surfing. It's the Sharkman episode in Animal Planet's "Bite Nights" series.