it's been a while since i had a physics class that dealt with quantum mechanics, but... here's what i remember. not only does time slow down as your velocity V approaches the speed of light C, your mass M also increases exponentially, meaning that it becomes harder to accelerate closer to C. it requires more energy (think E=MC^2) than before.
time travel forwards is perfectly possible. time travel backwards is possible in a few situations. ONE. pick up a book and read it, you can go back in time to the era of the story. TWO. Look up at the night sky. Everything you see is the result of light being given off years ago. Even the sun is old news. Theoretically, the sun could explode right now and we wouldnt know for about 8 minutes.
there's also that whole paradox thing. no offense to Stephen Hawking, but i dont think he's always all that brilliant. sure there's a lot of things that were thought to be impossible years ago that are common practice now (like flying) but some things seem to be utterly impossible. i say it's possible that we achieve farther and faster space flight, it's possible we colonize the Moon/Mars/Mercury, it's possible we set up some kind of space fleet and space stations. as for going backwards in time... i've had too much physics to believe in that