Every minute detail of human evolvement, with its accompanying experience, attendant with all of its historical mile marking accomplishments that men have learned to think of as progress, will be stood on its head. Immortality will require severe natal restrictions to accommodate an ideal population. In essence, death will be a thing of the past. Perhaps people will want a rest from life, so they'll "sleep" for a few centuries, preserving their DNA for future cloning: reconstruction, perhaps until the race occupies other planets in other galaxies, or learns time travel. Perhaps the sleeper will allow room for a new human being, unique, with an identity and personality of his own, and a new entity could be welcomed into the world.
As long as the race remains earthbound; restricted in population, the identification of ethical and spiritual values will be essential to the law's focus. Few will surrender immortality, so the exploration of inter-stellar space, and the colonization of other worlds, will be of primary importance. The dynamic of the world's first non-changing, non-ageing population will invite moral and creative stagnation. It will be imperative to get away from earth and settle other worlds.
Enormous advances in every discipline of science will allow the first off world settlements by 2100 AD, and that's probably a late estimate. Many institutions, not least those of belief, will be looked back on as pitiable afflictions, born of stubborn ignorance, perversely joining men's innate greed and chaining him to motive by blinding him to solution, in an evermore finite world.
Immortality will eliminate most human suffering. What, after all, would be the point of being immortal if you were only subject to a life of permanent misery? War, poverty, crime and most other self induced afflictions would simply melt away from human experience, like a molt that falls away, from a new, stronger body.
Ideas of solid, unchanging structure, of established order and ponderous ritual, of standing up to nature with brute strength, even the traditional shapes of things will give way to fluid, flexible adaptations in architecture, the clothing we wear, our entertainment, the way we cook and consume our food. A nomadic way of life will predominate as people migrate with the seasons, emulating nature as they learn to live within its limits.
Immortality will make what we had always thought of as permanent, suddenly temporary. Freedom from the unpredictability of death and its inevitability, will re-establish the flow of time in ways that people have no means of predicting. Suddenly, humanity will be faced with hundreds, if not thousands of questions. How will religious orthodoxy reorganize when the fear of death is gone? Simple questions, dealing with the sanctity of marriage and its, "till death do us part," clause will have to be resolved. Economic infrastructure, based today on estimated life time earnings, will become suddenly meaningless as will class distinction, and by extension money, as the only equality of value, immortality, is given as an entitlement.
It's because of our abbreviated lives that we struggle to fit all the things we want to do, into the little time there is to do them. Bitterness, the acute sense of failure that overtakes so many, results because of nothing more complicated than the repetitious experience of "That's all. Times up," as the carny opens the gate on your tilt-a-whirl before you're ready to get off. When science over-runs everything we thought we knew, our Gods, our institutions, all of our notions of governments before and since, even the ethical and moral regards we see as our values, the adjustment humanity will be forced to make will be the most traumatic, but bitter-sweet it has ever suffered.