Many plants multiply vegetatively. Essentially they fragment, and the fragments continue to survive, fragmenting again and again. This is a form of cloning and it makes estimating age very difficult..  Some trees create huge clones by root-sprouting and the clones may cover several hectares of land. The clone is commonly much older than any of the separate trees, even though they are all identical genetically. It is estimated that some clones are many thousands of years old. Also, many organisms create spores without any genetic recombination. They pass on the same genetic information that they have, thereby cloning themselves.  Some species of fungi have completely lost the ability to reproduce sexually, but have probably been around for millions of years. Most of us have some of these growing on our skin. So I think many plants and fungi have a different way of looking at age. They have discovered how to be immortal.

Quite interesting question, and two interesting answers too!

Joachim, I didn't know the facts on the Swedish spruce trees, so thank you. Quite interesting too from a biogeographical viewpoint! 

Martin, intuitively I disagree with you that the ramets of clones or the individuals of asexually propagating organisms in common are one individual organism, and I have been thinking why I feel this way. Talking about ramets of a clone you have two different stages, viz. the one where the ramet is connected to the whole, and the one in which the ramets loose their connection. At what age this breaking up is happening, depends on several causes, but one of them is the age of the ramet. As soon as a clone breaks up, the individual sprouts  have to be considered different individuals from a ecological point of view at least: they are not longer able to relocate nutrients and water, and they start to compete for resources. This is even more so talking about apomictic species: their individual 'parts' behave as individuals ecologically from the beginning. 

Yes, many plants and fungi (and bacteria and bellidoid rotifers, and....) have a different way of looking at age, I agree. They stretch our imagination. But I think the concept of 'age' by the OC relates more to the individual specimens than to the genetic package, I think...... So I stick to Joachims' Dalarna spruce trees as good candidates for the oldest living plants......

according to a common theory, plants have limintless growth.

Rense ... thankyou for a thoughtful response. I agree with you from an ecological perspective. Once separated the ramets are individuals and their individuality began on separation. But Agus has made a good point. The growth of plants is generally not limited by intrinsic factors, but by external forces. Furthermore, plant cells are generally 'totipotent', meaning that each cell can form all other types of cells. A leaf of a plant can be digested to release its individual cells, and then whole plants can be grown from each of the cells. In principle, this could go on for ever.

For this reason, I think plants do not regard their individuality in the same way that most vertebrate animals do. I would argue, for example, that each of the shoots of a tree regards itself as an individual, and that the ancient spruce tree in Sweden is thousands of individuals, from the perspective of the tree itself.  It is true that they all rely on the same root structure, but colonial organisms that rely on a colonial structure for their survival are very common in the world: corals, sponges, and so on.

I guess that my point boils down to the question itself, which is posed from a human perspective. Humans naturally look at individuality from a human perspective, but this is not wholly objective. The 'alternation of generations' that we find in plants illustrates this. When an individual moss plant produces its sporophyte, it has clearly produced a new individual, but to us it looks like part of the same individual. Each gamete of a moss expresses its individuality. So a moss would look at me and regard me not as one individual but as thousands.

... and then there are bamboos that form huge vegetative clones and are semelparous. Bamboos are remarkable in that the clones can be broken up and separated by thousands of kilometres, but flowering is apparently initiated by a genetic trigger, and the entire clone will flower, regardless of where its parts are. The clone dies after flowering, but the clone lives and multiplies for several decades before doing so.  Ecologically, they are actually all behaving as one individual, because their reproductive strategy has enormous ecological effects. For example, bamboo semelparity is considered one of the strongest risk factors for survival of isolated giant panda populations. While this is an exceptional case, it illustrates the fact that genetically determined behaviour contradicts the hypothesis that all genetically-identical clonal individuals behave ecologically as separate individuals. I have seen a dead clone of bamboo that had recently flowered. It covered several hectares on the top of a hill, and was a memorable sight.

For basic information on bamboo semelparity, see:     http://www.jstor.org/discover/10.1086/303243?uid=3739448&uid=2&uid=3737720&uid=4&sid=21104484911873 

For bamboo as a risk factor for giant panda populations, see:

http://www.bambubrasileiro.com/arquivos/Giant%20panda%20dynamics%20and%20bamboo%20-%20Carter%20et%20al%201999.pdf

Regarding the first part of the question "do plants die of old age?", the standard answer is that some do while others don't. Plants may be described as having "determinate growth" (they die of old age) or "indeterminate growth" (they do not die of old age and are generally killed by an environmental factor). This phenomenon is well is illustrated by tomatoes, some varieties of which are determinate while others are indeterminate.

Programmed cell death is a related phenomenon in both plants and animals, and is a necessary part of the process of development of form. During normal development, some cells are destined to die while others are destined to multiply.