Well, the cool thing about running at the speed of light, if that's possible, is that no one should ever be able to catch you, and not even one "moment" will pass forever. That poses kind of an interesting engineering question though...provided you could reach the speed of light, and time stops completely for you, how do you ever get out of light speed? It can't be a signal sent from something else--it could never reach you since it would be going at the same speed. Maybe if the signal came from your destination so that you "impacted it." But you can't do any calculations, either in your head or in a computer, since time is stopped....maybe you'd need a giant hay bail to stop you.
It's clear that if we accept relativistic theory as Einstein presents it, we're confronted with some really huge problems if we also want to accept FTL stuff. If we really want and believe in FTL, we should probably reject relativity and start over. The incredible predictive success of relativity very, very strongly suggests that it's a reasonably accurate portrayal of our world, however.
But, who knows. If you buy quantum mechanics, you can probably get away with assuming that anything is doable at some point. It's too complex for me (!), but really, I don't observe any of the properties of quantum mechanics in my day to day life. For instance, I've never ran at a telephone pole and divided into two separate, complete mes and reconnected at the other end (ala Penrose). Conversely, if I took an atomic clock on a fighter jet and left one synchronized at a TCU girl's dorm, I should be able to observe a difference in the two, reliably predicted by relativistic equation.
It's probably bad science, but whenever I see equations with infinities in them, hypothetical situations where time stops, particles blinking in and out of "nowhere," I just want to say hey--that's not the universe *I'M* living in. Supposedly, it's all based in empirical observation, but I just can't rationally imagine that universe. I tend to reject these claims, or at least fight them, mostly because I like to see it all add up in what I observe. And, I'm not a physicist, so I can get away with it without university hassle.