I came across an interesting concept and hypothesis, formulated by Michael Rose. Rose is a professor and researcher of evolutionary biology in Canada. He has published two books on the subject of aging; one of them titled Does Aging Stop?
The concept of "biological immortality" implies a point in time for an organism when it stops aging. This fact has been observed in many biological species. For example, there is a bush (a creosote bush) in the Mojave Desert that is older than 10,000 years. There are many other long-living species on the globe.
In practical terms biological immortality can be seen as a "plateau" where mortality stabilizes so a kind of immortality is achieved. That does not means that a person will not die (the true concept of immortality) but that the aging process is delayed so the body stabilizes and continues to live for a long period of time.
Rose has a "recipe" to achieve such immortality phase and it is very simple (as usually are the very important things in life): to live in an environment that is natural for humans. That means a lifestyle according to evolutionary concepts: a diet and physical activity that resembles that of our ancestors before the coming of the agriculture.
This means: to eat lean meats, fish, fruits and vegetables and avoid cereals, dairy, and modern processed food. Rose believes that during the early phase of a person's life the human body has all its power to hail the Neolithic diet (it is adapted to the Neolithic environment) but later on (as the person ages) such adaptative advantage is lost and diet starts to exert damage on our bodies. So, he thinks that for people over 40 (especially if the person has an Eurasian origin) it is possible to avoid such damages by returning to a Paleo lifestyle. (People from non-Eurasian origin are less adapted to the Neolithic and should start lifestyle changes at an earlier age, approx around 30 years-old). Basically he sees a primal/paleo lifestyle as a anti-aging therapy for the latest stages of human life. One that is cheap (compared to medical technology) and easy to start as soon as you decide to do it.