As Anthony Atala points out below, we have more people waiting for organ transplants than we have organs to give them. One of the solutions for this problem involves stem cells and triggering natural regeneration—basically, growing the organs out of the patients' own tissue. Atala's lab does just about everything you can imagine*, though not everything's ready for human trials yet.
This has a lot of potential, not only for saving lives and curing diseases like diabetes but possibly for giving immortality. If every part of the body could be rebuilt and put back into the body once it wears out, old age would be pretty much banished. (Until we achieve working brain transplants, we'll still have mental degeneration.)
His institute isn't the only one working on the issue, though. And we're making progress with stem cells, too.
* pretty sure they haven't done brains yet