You're speaking of Project Daedalus I believe, and the highest speed I saw for that was 12% of light speed. Of course, that was assuming that the trip was to a star within 5 or 6 light years; if you went further, you'd accelerate more and I'd guess you could possibly get into the 25%/35% range. That would require a larger ship or an additional stage, however. I remember reading some stuff from Carl Sagan and I think there were ships that were faster, but the technology to build them was still well in the future and Daedalus was the only one that could be built within the next few decades (he wrote that in the 70s, IIRC).
You make a great point about lifespan as well. There are many scientists who believe that biological immortality is not only possible, but it may happen in our lifetime. When I say biological immortality, that doesn't mean you're immune to diseases or accidents; it just means that you won't age and many "old age" afflictions would be eliminated as a result. You could still contract and die of AIDS, for example.