I'd give any organ that I could survive without, like one kidney, or part of my liver. I'd consider donating any of those to anyone I'm close enough to.
If it were something like my heart or stomach, I'd prefer to be dead before having those removed and given away. I would give those types of organs to anyone who needs 'em.
I would never ask to be given an organ, because somewhere out there there's someone who needs that organ more than me. Someone who can do a better service to society.
Blood, on the other hand, I would give in an instant if I didn't have sickle cell trait.