I'm not sure if there are any laws on it (and it would depend on what state you are in), but AFAIK it's yours to do what you want with. You just have to speak up and often that you want it because they are so in the pattern of disposing of them. I think there are certain religions that require their placentas to be buried. And if that's so, then they really can't deny folks their placentas without getting into a big legal/discrimination mess.
I would definitely mention it to your care providers and put it in your birth plan. And I would also call the hospital to ask them what their policy is on that sort of thing just to get an idea of if you'll even need to fight for this. I told my MW and doula and wrote it in our birth plan and it was no problem to bring ours home (I'm in CA). The only thing that might be an issue is if you have a c/s. Not sure, but I think I remember reading somewhere that with the anesthesia and all they have to treat it as medical waste. Don't quote me on that though.