I'm not sure that having people live forever would actually be a boon for the human race. The most obvious issue caused by increasing longevity is, as others have mentioned, overpopulation, but there are more subtle issues here as well.

For example, in countries that have a retirement age, what happens to that when people live forever? If people can maintain a productive state for longer, why should they leave the workforce? What about all the people who are currently counting the days until they're able to retire because they're at a job they hate?

It's easy to imagine everlasting life as being great from the perspective of a healthy, middle class perspective. For everyone else though, it might not be so great. For people struggling to make ends meet, or people with chronic health issues, living longer might not sound so great.

There's also the question of what a change like this would do to human advancement. It's a common trope in science fiction (and fantasy) that longer-lived species tend to be less 'driven' than shorter lived ones. The general line of reasoning is that with shorter life spans people tend to be more driven to make changes during their life, so that they can leave behind something that will last after they're dead and gone. What happens when you can just put something off to tomorrow indefinitely?