Unfortunately there is no one single website where any global citizen from anywhere can go sign up as an organ and/or tissue donor...let alone and ensure that his or her gifts will go to the people who need them the most.
Now there's an idea...but for now, I will list here the online national organ and tissue registries for every country I could find, and a couple of other relevant sites...Sorry I don't have more, either because I didn't find one yet, or because, alas, they don't exist (and need to!)
Please note the plea to people from all communities of color in the United States!
How Do I Become A Living Donor?
Bone Marrow Donors Worldwide
Taiwan & Beyond (Tzu Chi Foundation)
United States (OrganDonor.gov). To book a blood donation appointment in the US, please go to givelife.org . People of color in particular suffer and die needlessly because not enough people of color donate blood, other tissues, and organs. To learn more, please visit Help Us Save More Lives on the blood shortage, from MinorityNurse.com.
Umbilical Cord Blood Donation: Registries & Resources
Eurocord International Registry on Cord Blood Transplantation: FAQs
National Marrow Donor Program: How to Donate Cord Blood (has online cord blood registry that works with banks across the US and in Australia, France, Germany, Mexio, Spain, and Switzerland)
NHS (National Health Service) Cord Blood Bank (serves England and Wales)