This gets really interesting, and weird, if we're ever able to start making ships capable of approaching relativistic rates. You could arrive at the destination after 500 years, only to discover that humans colonized it 50,000 years ago.
For those who may not know, the speed of light isn't really a speed limit per se. If you have a button that gives you an acceleration of 1km/s, nothing stops you from hitting it 300,000 times in a row (with the speed of light being ~300,000km/s), or even a billion. Instead the entire universe begins to distort with distances becoming literally physically closer, and with rate of time itself also changing (length contraction + time dilation are the terms).
It has the interesting implication that if we could ever create a ship that "just" accelerates at 1g, you could travel essentially anywhere in the universe, even if it's billions of light years away, in a single human lifespan! [1] So for instance the distance to the closest galaxy, Canis Major, is about 25,000 light years. You could get there in our 1g ship in less than 20 years. Of course, 25,000 years would genuinely have passed in the interim, so you get all sorts of fun paradoxes and oddities. And the oddities are exponential, so you could travel a billion light years in 40 years.
And this isn't just hypothetical or whatever. Time dilation plays a major role in many things, like particle accelerators. Unstable emergent particles end up 'living' for far longer than they should thanks to the fact they're moving at near light speed relative to us, which means that time is [relatively] passing for it more slowly than for us.
[1] - http://convertalot.com/relativistic_star_ship_calculator.htm...