In a few years, 20 to 30 maybe, rejection of transplanted organs will be a thing of the past. Growing brand new organs from your own stem cells will be common place, and transplants will be all the rage just like robotic surgery is all the rage today..
In our children's lifetimes, or maybe I should say grandchildren for some guys here, cloning of your own organs for future replacement will be the norm for those who can afford it. For example when a person is in thier 30s or 40s, your own stem cells can be harvested, and through genetic manipulation, they can be used to clone all the various organs that go bad over time. You will be able to grow in a lab, organs like the heart, kidney, prostate, intestine, pancreas, etc. These will then be frozen until one is needed for replacement. Since it is your own cells, there will be no rejection. Then again, if we are this advanced with genetics to grow organs, we will probably already have a method to destroy cancer cells without harming regular cells, thus eliminating cancer as a killer all together, and not requiring transplants.