To the extent we find bugs that cause the brain to stop working properly over time, we'll need to find and fix those. That falls under "problems we'd love to have".
As for the question of whether people want to live for hundreds of years: if you don't want to live longer, you can easily stop. A surprisingly large number of people seem to rationalize the lack of immortality by claiming people won't want to live forever, which strikes me as sour grapes. Given an actual solution that allows people to live forever, the question becomes "do you want to die?", and I seriously doubt many people will say "yes".
(Also, if you think of immortality as "hundreds of years", I think you need to recalibrate your scale. I'd like a lifetime measured on a cosmological time scale, and I have no problem conceiving of ways to spend that time.)
Mostly, I'd never stop learning, and I'd apply everything I learned.
Consider the sum total of human knowledge today. Consider how small a fraction of it any one person knows.
Within the next month, I'll have completed a PhD in computer science. It took me years to learn the fundamentals of one field, plus years more to get practical experience by tinkering in numerous areas, plus years more to become an expert in one narrow area (scalable concurrent data structures) and advance the state of the art in that area. Take a look at http://matt.might.net/articles/phd-school-in-pictures/ to get a clearer picture of scale; now consider what a few million or billion lifetimes could produce, between research, practical work, exploration, and just good old-fashioned tinkering.
How many of those narrow areas exist in one field alone? How many more fields exist to explore? How many more will exist by that point? What happens when someone with expert-level knowledge in a pile of those fields starts applying them to each other? And most importantly, do you really think it ever stops?
Apart from that, I'd have plenty of time between learning everything and creating new things to enjoy the enormous amount of available entertainment created over the aeons, in all its various forms.
I think the future sounds awesome, and I want to see all of it. :)
Well, there are books, movies, TV shows, there is art and music and languages... and you haven't even touched on seriously studying different sciences up to a respectable level. I think it would benefit humanity a lot if people could have a much longer lifespan during which they can actually do things.
Think of all the time you could spend learning... also, think of all the time spent learning and experiences and eventually wisdom accumulated in even just one human being by the time they are 60, 70.... only to have it practically all lost forever once you die?
Also, wouldn't you just love to be alive only to see what the future will actually look like? it has been quite some time now since the last real paradigm-shift and real heavy impact innovation that changes our lives forever. I would love to see what is coming.
As for the question of whether people want to live for hundreds of years: if you don't want to live longer, you can easily stop. A surprisingly large number of people seem to rationalize the lack of immortality by claiming people won't want to live forever, which strikes me as sour grapes. Given an actual solution that allows people to live forever, the question becomes "do you want to die?", and I seriously doubt many people will say "yes".
(Also, if you think of immortality as "hundreds of years", I think you need to recalibrate your scale. I'd like a lifetime measured on a cosmological time scale, and I have no problem conceiving of ways to spend that time.)