I keep reading about scientists trying to prolong human life. They are recasting old age as a disease and trying to cure it. Assuming they succeed, we'll face some big problems. (And I'm going to ignore political/economic issues, like the fact that probably only rich people would wind up with 3000 year lifespans.)
I don't know what your chances are of dying in a horrible, painful accident (as opposed to dying of natural causes), but obviously you take a small risk every time you cross a street, drive a car, etc. Currently you have a fairly good chance of dying naturally, but that's just because you're "only" going to live 70 - 90 years. With each year you add, your chances of dying from UNnatural causes goes up. My guess is that if we all had a 5000 year life-span, most of us would wind up eventually being hit by a car (or whatever people ride around in thousands of years from now), eaten by a shark, murdered, etc. It's only the decay of our bodies that saves most of us from these fates.
You'd have to get used to your loved ones dying horribly, too. So when you got married or had kids, you'd have to resign yourself to the fact that (if you don't go first), you are probably going to see your family die in a plane crash or earthquake.
Also, there's the problem of "hard drive space." Once you cure cancer, stop body-parts from decaying, etc., what are you going to do about memory? Our storage space is vast, but it's not infinite. When we're 3525 years old, will we remember anything from when we were 15? Or will we remember EVERYTHING from when we were 15 but nothing from five minutes ago?
I must admit, though -- as a childless atheist, who doesn't believe in any sort of afterlife and won't be leaving any of his genes behind -- I would LOVE to stick around for a few more hundred years. Just to see how things turn out.