opt out, because many relatives just aren't thinking about it when their family member dies, and the window of oportunity is very small.
My mother in law died suddenly after an asthma attack many years ago. I don't think that organ donation was mentioned at the time. When I asked my fil (a few years later) he said that he probably would have liked to be able to donate. As it happened she had multiple organ failure, so it would probably only have been the corneas, but that still could have helped someone. Of course it would require checks and balances, but I don't think that it would automatically mean that your body belonged "to the state", as we are not talking about giving your body to science / experiments etc.
Many people really don't like talking or thinking about things related to death, and that's probably the largest reason that people aren't on the list. Maybe there should be an automatic appointment generated for everyone at 18 or so, so that you got put on the list after someone talks to you about it, so that you can have an "informed opt out". Obviously children would have to be with parental consent, but again maybe a conversation could happen? It sounds a bit brutal, but I know that it is difficult to find organs for children.
My neice died wilst waiting for a liver transplant, and I started thinking about a living donation at the time (unfortunately she died very soon after). I think that the idea of being able to save someone's life is fantastic. I'm also on the Anthony Nolan bone marrow transplant list. If anyone is thinking about that check out their web-site here