Further thoughts on immortality
Another point occurs to me, having to do with demographics. Currently, certain demographic groups (for example, certain fundamentalist religious groups) have much higher birthrates than the population at large. The net result is a slow increase in the proportion of the population belonging to those groups, which may or may not be counteracted by other factors. However, the development of radical life extension would likely greatly accelerate the rate of that drift.
Let's do some math. Currently, most Americans choose to have approximately 2 children over the course of their 70 year lives (for a net reproductive rate of 1 child every 35 years), while some choose to have as many as possible. Typically, "as many as possible" means 6 to 10 children over the course of a 70 year life (for a net reproductive rate of 1 child every 9 years). So, ignoring other factors, children of the prolific parents will be over-represented in their generation by a factor of 4.
Consider, though, what happens if you introduce radical life extension (which probably means that all adults are perpetually of reproductive age). The population at large will likely maintain or reduce its reproductive rate of 1 child per 35 years. People committed to having as many children as possible, however, will probably be able to achieve a sustained rate of 1 child every 2 years. This means that children of prolific parents will now be over-represented in their generation by a factor of 17, or more than 4 times the present-day multiplier.
Whether this is a desirable outcome is left as an exercise for the reader.