Hi meucat,
In fact, according to some theories, we COULD live eternally, without aging, it's not physiologically impossible, in fact some multicellular organisms in many phyla doesn't seems to age. The reason we get old and die is probably because it's advantageous from an evolutionary point of view (I know it sound strange at first).
What you need to ask is; it is advantageous to age/die for the individual or his genes. At first it doesn't seem so. If you don't age, you could reproduce longer, have more children, and therefore making a greater contribution to the next generation (increasing fitness).
You must understand that all organism tend to increase their fitness (their genetic contribution to the next generation) and
do not care about "species survival". To increase fitness, reproducing early is better than late, because your children will
have children faster and your genetic contribution to next generations would be greater (By the way this is the subject of a subdiscipline of evolutionary ecology; life history evolution).
Medawar (1952) proposed that, as late reproduction does not contribute much to fitness, the selection against genes affecting individuals late in life is very weak, so they accumulate.
Another explanations, probably complementary to Medawar's theory, made by Williams (1957) is that some genes are affecting positively the individuals early in life but negatively later in life, contribution to the fitness of the individual at the expanse of his long term survival. We call that an antagonistic pleiotropy. The existence of those genes were confirmed by many experiments (Rose and Charlesworth, 1981; Luckinbill et al, 1984 and Leroi et al, 1994)
Sure, it doesn't explain the physiological reason for aging, in fact, according to those theories, aging is the consequence of diverse genetical and physiological causes. However it explain WHY, in essence, we experience senescence.
References;
Roff, D.A. 2002. Life History Evolution. Sinauer Associates. The best book on life history evolution, lots of maths
Stearns, S.C. 1992. The Evolution of Life Histories. Oxford University Press.
Fox, C.W., Roff, D.A. and Fairbairn, D.J. (Editors). 2001. Evolutionary Ecology: Concepts and Case Studies. Oxford University Press. Have a whole chapter on senescence.
Medawar, P.B. 1952. An Unsolves Problem in Biology. H.K.Lewis, London.
Williams, G.C. 1957. Pleiotropy, natural selection, and the evolution of senescence. Evolution, 11, 398-411.
Leroi, A.M. Chippindale, A.K., and Rose, M.R. 1994. Long term laboratory evolution of a genetic life-history trade-off in Drosophila melanogaster. I. The role of genotype-by-environment interaction. Evolution, 48, 1244-1257.
Luckinbill, L.S., Arking, R., Clare, M.J., Cirocco, W.C. and Buck, S.A. 1984. Selection for delayed senescence in Drosophila melanogaster. Evolution, 38, 996-1003.
Rose, M.R., and Charlesworth, B. 1981. Genetics of life history in Drosophila melagaster. II. Exploratory experiments. Genetics, 97, 187-196.