What threatens to make realistic SF impossible is that space is big. The gulf between things is so vast that there's no way to wrap our frames of reference around it. Traveling to another star isn't like traveling to another country or another continent; no continent is far enough away for that comparison to make sense. What does "travel" even mean if it takes a lifetime to move a couple of short steps away from where you started?
The basic problem, if you haven't been thinking about the issue, is this: modern physics can't conceive of any speed faster than that of light, and it's impossible for matter approaching the speed of light to continue to behave as matter should. This is important for science fiction because your characters are very likely to be made of matter.
And remember the unimaginable vastness of space? It gets even tougher when you realize that light still takes decades or centuries to reach even the closest foreign stars.
But that's why
they call it science fiction: when reality is broken, you make up
science to fix it. Authors have tried this many different ways, but it usually comes down to the same sort of technological hand-waving. The usual solution is warp drive, jump drive, hyperdrive, or any of a dozen other names for Faster-Than-Light technology that requires not only
undreamt-of machinery but also the assumption that our understanding of
physics is extremely and conveniently wrong.
This is necessary. Take the FTL out of science fiction and you don't get far.
Most of the time, an SF story simply insists on FTL and leaves it at that. Star Trek's warp drive is the classic example: we have awesome engines that get us where we're going as quickly as the plot requires. Occasionally we run out of Dilithium Crystals, or Scotty tells us he can't give us any more power, or Tribbles get into the engine room, but otherwise the mechanism and its implications are invisible. Warp speed means never having to think about scale. Space is no bigger than California.
Battlestar Galactica's jump drive works pretty much the same way, although some effort is made at consistent limitations. Apparently it takes some time for a ship to calculate a leap, and the show's premise requires coordinating a whole fleet of ships (some of them rustbuckets) jumping individually to the same spot. Tension in the favorite first-season episode "33" is built around the need to keep one jump ahead of the pursuing Cylons. In BG's early episodes, at least, FTL travel looks like something that makes passengers nervous, as if no one ever really gets used to whatever it does to you.
The most interesting treatments of FTL imagine it as something other than just fast travel. The interstellar society of Frank Herbert's Dune is made possible through the power of the spice melange, which allows Spacing Guild navigators to psychically "fold space." This would be just another jump drive if the political economics of spice and the mental powers it facilitates weren't central to the plot and to the protagonist's own story.
Norman Spinrad's under-appreciated The Void Captain's Tale does something similar, except with orgasms.
Some time ago I wrote a science fiction novel set two hundred years in the future. I wanted to avoid space opera--it wasn't that kind of story--and I wanted to keep things as realistic as I could. At the same time, I needed another planet for the action. I settled on a scenario in which humanity has made its first, halting steps among the stars, but things are going slowly. The novel's action takes place on mankind's first (and already failed) extrasolar colony.
I kept the math simple. The colony world orbits a star twenty light years from Earth, and I arbitrarily decided that my future technology could move a spaceship at half the speed of light. This means that a one-way trip requires forty years of travel, something conceivable if the people making the journey are put into suspended animation and awakened when they reach their destination. Communication is also limited by distance: even light-speed messages from the colony take twenty years to reach back to Earth, and then you wait twenty more for the reply to your original message, now half a lifetime out-of-date.
What this gives you is a universe where space colonization is feasible but where the colonists are very much on their own. This kind of science fiction is sometimes compared to the sixteenth- and seventeenth-century "Age of Sail," when travel was difficult, dangerous, infrequent, and often one-way, but still possible. Interstellar distances push these difficulties to the limit of what human beings might be willing to undertake, but perhaps not beyond them.
I tried to make use of the distance in other ways. All the time required for travel allowed for the development of a secret history unknown to the travelers before their arrival, and the distance, isolation, and sense of loss were thematically useful from the beginning. Most of all, it gave me a story that focused on what the characters had to do and decide rather than on the magic their machines were capable of. And anyway, warp drive would have solved my novel in three or four pages, and where's the fun in that?
I'm rewriting this novel now in the hope of making it more what I want it to be: out with the tiresome expositions, in with a little more action, over there with some characters taking up too much of the floor. But I won't be changing the timeline or the technology. That's the part of the story that has always made just the right amount of sense.
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EDIT: A few days after this post, Slate.com produced a neat animated graph on SF travel times.
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