No, we're not quite there, yet. But it looks like we're much closer than we were:

SCIENTISTS have created a beating heart in the laboratory in a breakthrough that could allow doctors one day to make a range of organs for transplant almost from scratch.

The procedure involved stripping all the existing cells from a dead heart so that only the protein “skeleton” that created its shape was left.

Then the skeleton was seeded with live “progenitor” cells, which multiplied and grew back over it, eventually linking together into a new organ. Such cells are involved in the formative stages of specialised types of tissue such as those found in the heart.

The research, by scientists at the University of Minnesota, has so far been done only with rats and pigs and is highly experimental. It is unlikely to be applied to humans for years.
However, Professor Doris Taylor, director of the university’s centre for cardiovascular repair, believes it could be a significant step towards creating custom-built hearts, blood vessels and other organs for people with serious illness.

The big advantage of such an approach is that organs so built would use stem cells taken from the patient so the body’s immune system would not reject them.

“The idea would be to develop transplantable blood vessels or whole organs that are made from your own cells,” Taylor said. “It opens a door to the notion that you can make any organ - kidney, liver or pancreas. You name it and we hope we can make it.”

The promise of this procedure would be difficult to overstate. To be able to give someone whose body has been devastated by heart or kidney disease a healthy organ with no need for a donor and with no real risk that that the transplanted organ will be rejected...that's huge. I wonder if the same or a similar procedure could be used to re-grow seemingly simpler structures such as bones and teeth? Also, could the same or a similar process be used to replace sections of a damaged spinal cord?

Plus, I have to wonder what the possible life extension implications this development might have. There's the question of the "age" of the new organ. If I'm 45 and I have a new heart grown in this manner and transplanted in, is it a 45 year old heart? Or is it younger? If younger, what would happen if a person swapped in a new pituitary gland grown in this manner? The new glad might start sending signals out to the older body telling it that it's younger than it really is. Of course, this won't repair accumulated cell damage, but this perhaps this could at least slow down the process of a body shutting itself down.