TreeLogic's observation about the differences in the usual age ranges of trees is a good one. We usually think of tree age as being the longevity of a particular stem. If those river birches in TL's post fall apart at 40 years, yet keep sprouting from the roots or the broken butt of the stem, they could keep that genetic individual going for a long time. That's the basis for folks calling a specific aspen clone "thousands of years" old, even though none of the stems may be more than 100. I just read the link from jomoco. That's my point. The grove is estimated at 80,000 years...but none of the stems may be more than 200 years old, or less.
Sure, I try to keep it commonsensical and look at ages of individual stems, but that's not the only way to look at it.
BBBTree touches on the corruption of chromosomes and DNA sequences from many generations of copying. That's what most cell biology texts teach, and I'm inclined to believe it. But true enough, the model systems that have been studied in the detail necessary to be sure have been pretty few in number.
Back to TreeLogic, all trees have to allocate their resources for competing needs of growth vs. defense and safety vs. efficiency. Some strategies are great for colonizing disturbed landscapes fast, getting a quick foothold, growing tall, and dying and decaying early. Other trees don't like disturbance at all, do OK in shade, and invest a lot in natural wood preservatives to keep the wood intact, even after the tree is dead.
No one strategy is best, it depends where you are.
As for whether a tree would live forever if protected from harm, starvation, or too much of good things...I guess that is taken as a matter of faith, whichever way you go. For me, as that will likely never happen, I don't spend much time on it!