In my case, nobody gets my organs... nobody gets my bone marrow either, or my blood, or my reproductive material... or my body for lab experiments, dead or not.
That's just my personal choice, and I see no reason as to why I can't have it; out of the billions of people on Earth, there are sure enough willing to donate their organs to those that need them. I'm just not one of them. My body belongs to me, and as horrible as it sounds, I don't care about helping others, as sick or as unfortunate as they may be, by... being used as 'replacement parts'.
Maybe that's just because of my dislike of organ transplants in general, with the lifestyle impacts, the immune-system destroying drugs and soforth- sure, it's better than being dead (or at the least being very ill), but it's almost like... a lesser of two evils. It really makes actual, custom-made organs grown from stem cells or the like that much more attractive- now that might be a long way off, but we can already grow [ame="http://en.wikipedia.org/wiki/Artificial_urinary_bladder"]simpler organs[/ame], and even conducting biological repairs of damaged or failing organs could be massively helpful.
Until then, some sort of opt-out system would be a good idea, but only if the societal environment existed to deal with it properly; it is clearly ideal for a place such as Slovenia, but not in the Bosnian healthcare system described by jedidia, and probably not in countries such as South Africa or worse, where sadly most people only have a vague idea of what an organ transplant is.