It is possible to 'travel' forward in time if you move at a speed close to the speed of light.
This is what Stephen Hawking has to say on the matter:
"You just have to travel very, very fast. Much faster even than the speed required to avoid being sucked into a black hole. This is due to another strange fact about the universe. There's a cosmic speed limit, 186,000 miles per second, also known as the speed of light. Nothing can exceed that speed. It's one of the best established principles in science. Believe it or not, travelling at near the speed of light transports you to the future.
To explain why, let's dream up a science-fiction transportation system. Imagine a track that goes right around Earth, a track for a superfast train. We're going to use this imaginary train to get as close as possible to the speed of light and see how it becomes a time machine. On board are passengers with a one-way ticket to the future. The train begins to accelerate, faster and faster. Soon it's circling the Earth over and over again.
To approach the speed of light means circling the Earth pretty fast. Seven times a second. But no matter how much power the train has, it can never quite reach the speed of light, since the laws of physics forbid it. Instead, let's say it gets close, just shy of that ultimate speed. Now something extraordinary happens. Time starts flowing slowly on board relative to the rest of the world, just like near the black hole, only more so. Everything on the train is in slow motion.
This happens to protect the speed limit, and it's not hard to see why. Imagine a child running forwards up the train. Her forward speed is added to the speed of the train, so couldn't she break the speed limit simply by accident? The answer is no. The laws of nature prevent the possibility by slowing down time onboard.
Now she can't run fast enough to break the limit. Time will always slow down just enough to protect the speed limit. And from that fact comes the possibility of travelling many years into the future."
(credit http://www.dailymail.co.uk/home/moslive/article-1269288/STEPHEN-HAWKING-How-build-time-machine.html)
In layman's terms, this is what he meant.
The train is moving at a rate just shy of the speed of light. The speed of light (186,000 miles per second) is the cosmic speed limit. Nothing can ever exceed that speed, this is why time dilation occurs close to this speed. If time moved as normal on board the train, the people inside the train (whilst moving at close to the speed of light)* would exceed this cosmic speed limit because the would be moving on board this train.
Time would slow down on the train to prevent this law being broken, and this is what would cause 'time travel'. Technically is not 'travel' because you are not moving from one time frame to another, but for a week or so you spent inside the speed-of-light-train a whopping 100 years would have passed to everyone else on the planet.
*Taking into account that moving even a fraction of this speed would kill everyone on board due to G-forces.
Now obviously building a train that would move this fast is impossible, but perhaps many years down the line scientists will have found a way to use this knowledge and invent a time machine, ethical problems aside.
Another possible way is the use of gravitational time dilation, Einstein's general theory of relativity states that time travels slower in deeper gravitational wells.
If a crew of astronauts orbited the black hole in the centre of our galaxy, time for them relative to the time for us on Earth would be about half though for obvious reasons this isn't practical.
So final verdict, Time Travel; very difficult but not quite impossible.
