With a nuclear thermal rocket you could definitely reach a tenth of the speed of light. It would take 40 years, though [to reach Alpha Centauri], which is a long time. You’d have to start off not too old if you wanted to see it.
There are some interesting things I’ve seen lately about warp drives. [Harold White’s space warp experiments. Covered by NBF] You can’t exceed the speed of light but you can warp space and effectively travel many times the speed of light. That’s kind of exciting. People have found increasingly smarter ways of minimising the energy required [to warp space]. Before, you would need the mass-energy of Jupiter.
Sure Spacex would love to have a warp drive, but I’m not going to hold my breath on that one.