Essentially, travelling that fast is reckoned impossible because it's the maximum speed anything can travel. (And that’s disregarding the dilation of time, as described by Einstein and sung about by Brian May in ’39).
This matters because the galaxy is so widely spread out that travelling almost anywhere beyond the solar system requires a very fast system of travel. Voyager was launched in 1977, and only reached the edge of the solar system last year (http://www.bbc.co.uk/news/science-environment-13704153).
So, there are a few options:
Ignore science: this is the simplest method of resolving the problem. Just use warp speed or hyperspace or whatever you want to call it, and don’t bother explaining how it works. The only potential problem is if you’re trying to make your sci-fi story as realistic (scientifically) as possible.
Alien technology: pretty similar to the above, but with a crucial difference. A system of gates (as used in the very enjoyable Stargate SG-1 series), for example, enables travel over huge distances but does not allow the human race to have a similar tech level in other areas. So, you get the travel options but can keep everything else more realistic and lower tech.
Don’t go that far: keeping the human race confined to the solar system, and perhaps one or two of the nearest stars reached by sleeper ships, can work perfectly well. Mining on other planets and moons (or the asteroid belt), wars over territory and so forth doesn’t really need a far flung empire.
The actual decision made doesn’t especially matter provided it doesn’t jar with the rest of the universe the writer’s created. Maximum realism of 27th century firearms coupled with a magic box with Light Speed Engine written on it would rather break immersion.
I tend not to read as much sci-fi as fantasy. The last books I read were Toby Frost’s excellent Space Captain Smith series. This is probably because I prefer history to science, and find the general fantasy worlds (medieval England, Rome, Byzantium, Middle-Earth etc) more to my taste. That said, I think I might try hunting down some new sci-fi.