If there's one thing that science fiction is nearly universal on, it's that traveling at or beyond the speed of light looks really freakin' awesome. Star Trek had those rainbow star lines zipping by, Star Wars had something similar, and Spaceballs went all the way to plaid. The reality, unfortunately, may not be nearly as cool.
Physics students at the University of Leicester decided to buzzkill the entire sci-fi genre by going and calculating what would happen if you were to kick a spaceship up to the speed of light and look out a window. This is about the extent of what you'd see:
Yeah. Boresville. The reason this is all you'd get is because of the Doppler effect, which says that the frequency of a wave changes as you move relative to its source. You've heard the Doppler effect in action plenty of times: it's what causes a police siren to change from high pitch to low pitch as the police car drives past you. As the car approaches, the sound waves it's emitting bunch together, increasing their frequency and consequently their pitch. And as the car passes and drives away, the sound waves spread apart, decreasing their frequency and pitch.
This same thing happens with light waves too: moving towards a light-emitting object (like a star) causes the light waves to bunch up a bit, increasing their frequency (and decreasing their wavelength) and shifting the light towards the bluer end of the spectrum. Moving away from a light-emitting object runs the whole thing backwards, leading to a shift to the red, which is how we know the Universe is expanding: distant galaxies are all redshifted, meaning that they're moving away from us.
So anyway, back to light speed. If you're moving at (say) 99.99995 percent of the speed of light, which is what these students used for their calculations, light from stars will be shifted so far towards the blue end of the spectrum that it'll end up way past what we can see with our eyes, turning into x-rays that are effectively invisible. Meanwhile, very long wavelength light that we ordinarily can't see, like cosmic background radiation, is shifted up into the visible. So essentially, stars disappear, and all we see is the leftover glow from the Big Bang as a formless blob of light.
We are of course obligated to point out that none of the spaceships in sci-fi are traveling at lightspeed; they're all traveling beyond lightspeed. So maybe there's just a transient flash of cosmic background radiation, before something far more interesting (and ludicrous) happens once you break the lightspeed barrier.