Maybe 500 years by today's behavioral standards. I assume that if people were told you could live ~forever barring an accident leading to your death, many people in society would behave VERY differently. The risk profile of you or me getting in a car to drive to the store is VERY different than someone with age-and-sickness-proof-but-accident-vulnerable immortality.
Incidentally this is one reason why people in the past seemed braver than now and did crazier things. When your life expectancy is 25, you take a lot more risks.
