It turns out it's not that easy, at least in Canada. There is no central registration: you have to register with a school of anatomy. Then after you die your family or estate has to pay to have your body shipped to the school, and it could be expensive if you die far away from the school you use.
In my case, I live in Waterloo, and have a few problems. The first is that the local anatomy school is not one I want to donate to; it's for kinesiology students and allows non-majors to work with cadavers, and I don't want to donate to it. The closest medical school that takes bodies is in Toronto. The second problem is that I can't rely on having any family alive when I die to follow my wishes, so to arrange for having my body shipped to a school, I need to change my will. Also, I travel a lot and work in different cities, so the shipping could be a real issue.
But the biggest problem with Ontario's body donation policy is that it can't be integrated with organ and tissue donation. Other than your eyes, if you donate your body to an anatomy school then you cannot donate any organs or tissues to help sick people.
Another problem is that you can't just register to donate your body - you have to contact a school and ask to be sent a package of information. I don't want to read about what they do with the bodies or how they treat them (and I am very sympathetic to medical students who may cope with the difficulty of learning to cut human flesh by making light of the bodies) - I just want to sign up, at a distance, impartially.
All this might explain why schools of anatomy don't get enough bodies. (They get about 300 donations a year, in total, at the ten schools that are looking for bodies.)
It's a shame. For example, a few years ago I read about research into female sexual organs and some breakthroughs in understanding how female orgasms work. The researcher said that very little was known about the subject because researchers virtually never had young female cadavers to examine, and the anatomy of elderly women is quite different.
Ontario organ and tissue donation: Trillium Gift of Life Network
Office of the Chief Coroner (Toronto) 1-877-991-9959 or 416-314-4000