It is interesting to note that death is perceived as a 'natural law', that all living things must die. This is actually incorrect. Most people think of animals and plants when they think of 'life', but there is so much more than that.
Micro-organisms are known for their longevity. Given enough resources, bacteria can grow forever, but it is hard to determine an 'individual' bacterium lives on forever. That's easier to spot with multicellular organisms, such as slime molds and fungi.
Fungi, for example, are modular organisms. That basically means you can split an individual in two, and both will grow on. The opposite are unitary organisms, such as vertebrates. If you give a fungus enough resources, it will grow on and on. Most fungi are in fact immortal. Only external factors (lack of resources, disease, etc) can cause a fungus to die.
Some fungi are mortal however. They usually live in an environment that is not very sustainable and exists only for a short period of time (dung, for example). When grown in lab conditions with enough resources and such, growth will stop after a few weeks. Podospora anserina is one such fungus.
But even here, mortality is not a certain destiny. Some mutants have a longer lifespan, months instead of weeks, and some have grown for more than 15 years and are still alive and well. So it seems that 'all living things must die' is not true at all. (interesting note: most of these mutations come with a side effect, like lowered or no fertility)
But why is death (or rather aging) so common? I have no exact answer, although some ideas have already mentioned in this thread. Very likely death is an effect of having a limited lifespan by external factors (an almost certainty in nature), and may be a pleiotropic effect. I think it is a price we have to pay for the way our bodies are built, but I think it is a price worth paying.
For more information on aging,
this site is a nice, though not perfect overview.
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