...Lord of the Rings style Elves, that is. What's so special about them Elves? Well, they live forever, of course! To be more specific, they are immune to the effects of aging and disease, but can be killed via more direct means.
The SENS movement views the human body as essentially a machine (albeit a very complicated one). Under this view, we can, at least in principle, develop techniques to repair all age-related damages that our bodies accumulate over the years. As we diagnose and solve more exotic forms of cellular damage and diseases (which might be currently irrelevant since we still die from more obvious causes), we might perhaps actually achieve longevity escape velocity. You can read an excerpt from Aubrey de Grey's book here (or if I like you enough, you can borrow my autographed copy).
For those who are curious, here are a bunch of recent articles showing a very limited snapshot of our current progress. It's certainly a very exciting time to be alive (although being born later would be even better).
So let's assume we're amongst the lucky ones who can live, if not indefinitely, then at least for a very long time. What does that imply? Well, for one, the Elves in LOTR rarely produced offspring. While many would consider this tragic, I expect almost everyone (at least in the developed world) to agree that having around two kids is preferable to having ten kids. The arguments in favor of two over ten tend to revolve around quality of life (both for the parents and for the potential children). Once our standard of living increases dramatically, one can make the same arguments for preferring to have almost zero children over having two.
But fear not, for I expect we'll be having a decent number of kids for many years to come. This leads to another interesting situation. In LOTR, Elves spend most of their lives in healthy adulthood. As such, parents and children are more or less peers (trivia: Galadriel is Elrond's mother-in-law and also his first cousin thrice removed). We see a hint of this effect already in our society; these days, parents and children might jointly enjoy 10-20 years of healthy adulthood together. So I expect this dimension of society to make a relatively smooth transition.
A particularly interesting issue is power (and career paths). In the LOTR, all the elder Elves stay in power until they are killed. Tolkien clearly wasn't trying to predict future social norms when creating his mythological world and its long-lived Elvish peoples, but it's interesting (at least to this Tolkien fan) to use as a point of contrast. A static chain of command doesn't sound very appealing. On the flip side, it seems unlikely that we could all retire (until we die) unless our productivity skyrockets at nigh-unbelievable rates, so some other solution is probably required. The most obvious one is for people to choose a line of work for a few years, take a few years off, and then rinse and repeat. Sounds pretty enticing, eh?
I hate to end this post on a downer, but the last issue we'll be covering is inequality. In the LOTR, many Elves looked down on mortal Men, whose lives are but a flicker compared to the eternal flame. On our side, not everyone has enjoyed the fruits of capitalism and its remarkable ability to spur innovation and progress. How can we bridge this gap? Despite the various disparities found within the developed world, social mobility is very possible for people with sufficient skill and dedication. But such opportunities rarely present themselves for those stuck in the bottom billion. Will we also live in a world with second class citizens? Will privilege of birth determine whether one might live forty or a thousand years? The wisest Elves looked beyond the frailties which plagued Mortal Men and formed bonds of friendship for the benefit of both races (e.g., the Half-Elven). Perhaps we can do the same.