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Because of relativistic time dilation, the time would seem to be less for the spaceship crew. At very near the speed of light, the spaceship could travel millions of light years within a human life time for the crew. Of course the time here on earth would still be millions of years, so there would probably be no one here to welcome them back.
As I understand it--and I am certainly no expert on this subject--the relativistic effects are not too extreme below a velocity that is fairly close to that of light. I seem to recall that the problem with taking advantage of these effects by getting very close to the speed of light is that as you get closer to it, the amount of energy needed to keep accelerating starts to get fantastically large.