First off, if you eat shark, you're a bad person who should feel bad for contributing to the decline of a species that helps keep our scallops and lobster plentiful. Also, here's another reason why you probably shouldn't eat it: In China it might not actually be shark fin and it might actually poison you.
The investigative report exposing the shark fin fraud comes from Cantonese speaking CCTV. They estimate that upwards of 40% of all shark fin consumed in China might actually be fake. Worse, the chemicals that people use to make their concoctions have the texture of shark fin aren't exactly regulated by the government and have been linked to lung and organ damage.
Dave Lieberman over at the OC Weekly lays out the salient points: Real shark fin is served more as a status symbol than for it's actual qualities, a single fin can go for around $50. The fin itself is virtually tasteless and destined for only one dish, shark fin soup, where it favored for it's ability to impart a gelatinous texture to the soup. It's possible that you could achieve a similar effect with diced rubber band and corn starch. That might explain the fake shark fin poisonings.
The consumption of shark fin isn't actually banned in America, it's only the favored method of obtaining fins which is illegal. Finning involves hauling shark out of the water, slashing off all of its fins and then dumping it back into the ocean where it flops around until it starves, gets eaten by something else or bleeds out.
If you'd like to try shark fin out for yourself without the possibility of poisoning or questionable eating ethics, here's a handy recipe for faux shark fin soup.