My parents both decided to donate their bodies to medical science. When my dad died in the September we were told that the fridges were full and they couldn't take him - the university had been on holiday for 3 months, so they hadn't been using any.
So if you are going to do it, you'd better make sure you die when they can actually take you! (We eventually buried him, and then my mum decided not to go ahead with her donation).
Funnily enough, I read an article only about a week ago on the idea of donating your body, and it seemed as if they were actually needing people to do it nowadays (my dad died in 1985). I must admit the idea appeals to me.