I asked a question about immortality of hydra and learned good things about senescence. Now I would like to know about immortality in plants, if there is some kind of immortality in plants and how this occurs - how does it protect itself from senescence?
Since meristems (the parts of plants from which growth happens) are constantly creating new stem cells, plants have a theoretical capacity for immortality. Of course, in practice, the vast majority of plants still senesce and die. But there are some notable exceptions such as bristlecone pines and quaking aspens which live for thousands of years. If you consider new individuals produced through clonal reproduction to be extensions of the original individual, then even more plants could be seen as immortal.
I can find no examples of immortal plants, but then again immortality is rather hard to prove, it's rather like trying to prove that space will never turn in to a pony - as long as time exists it could still occur, only if you go beyond the end of all time would you be able to say that it has or has not happened but then time would no longer exist and nor would space/the pony.
However, for examples of long lived plants it is perhaps best to look at trees - there are some species that live a long time and they can easily be aged. Here is a list of oldest known trees. It is difficult to tell how old these trees can become, and thus whether they are "immortal", because anything that lives that long is likely to encounter sources of extrinsic mortality during it's lifetime - predation, deforestation, extreme weather, erosion, natural disasters, contaminants, humans, disease, parasites etc. (rather than intrinsic dying of old age).
A lot of plants go through some kind of apoptosis, where cells are programmed to die. Plants such as annuals, biennials etc. die after a few months or years in a programmed way. It is difficult to say whether long lived species of trees would do the same after a few thousand years of life, because we just don't get to see many reach that stage of life, or if the mechanisms causing it have been suppressed (which could explain their long life).
Luke has posted a very thorough answer on the cellular and genetic aging of plants here. And to quote him:
Wikipedia has some very good pages on the evolution of senescence & aging. This article has also a good section on plant aging and I hope you can access it.
and finally, if you want to have a laugh, take a look at this entry on plant immortality and aging from creationwiki.org...
Some great clear science there, well done creationists... but it's just plain wrong.
In addition to the above answers, the answer to your question also depends on your definition of immortality. There are a number of clonal organisms (the most famous of which is probably Pando, a quaking aspen https://en.wikipedia.org/wiki/Pando_%28tree%29 ) where there is a large area, sometimes multiple square miles, where individual shoots are sent above ground, giving anyone in the area the impression of a forest, but all of the trees are connected underground in one single large root system.
Such an organism could certainly be considered immortal, as its stems will constantly die off and be replaced by new organic material, enabling the network as a whole to live for tens of thousands of years (so far).