Time travel is possible according to Relativity. According to Relativity (and I'm sure Pawna will correct me if I'm wrong), the faster an object travels, the more time will distort and begin to slow down as it nears the speed of light. Hence, once you break the speed of light threshold, you would be traveling backwards in time. However, Einstein says that nothing can travel faster than the speed of light. This is because the faster an object travels, the more mass it gains and the heavier it becomes. The heavier it becomes, the more it will begin to slow down. For something to travel at, or faster than, the speed of light, it would need infinite thrust (because the gain in mass would also be infinite), which is impossible.
So how do we measure the affect of speed on time? Well, it's relative to the point of view of the individual.
Imagine two people, Bill and Bob. Bill will be traveling close to the speed of light and Bob will be observing. Bill has a bouncy ball that he can position above the ground so that, when he drops it, it takes precisely 0.5 seconds to fall to the ground and 0.5 seconds to bounce back up to his hand. When he is stationary, Bill drops the ball and catches it again. To both Bill and Bob, the ball has traveled in a straight line and took exactly one second to fall and bounce back up to his hand. Then Bill sets off and, at 100MPH, drops the ball again. From Bill's perspective, the ball falls and bounces up in a straight line again while, to Bob, there is a slight v in the ball's trajectory. Now Bill is traveling at close to the speed of light and drops the ball again. From his perspective, the ball again drops and bounces up in a straight line. However, from Bob's perspective, the V shape of the ball's trajectory would not only stretch the length of your computer screen but probably from one side of the room you are in to the other.
In other words, from Bob's perspective, the one second it takes for the ball to fall to the ground and bounce back up again has stretched and is now taking much longer to travel its course. Yet it still takes the same amount of time for Bill. Therefore, from Bob's perspective, Bill is traveling much slower through time than he is (yes, I know that if Bill was traveling close to the speed of light then Bob wouldn't be able to see him at all. This is just a demonstration, so use your imagination people). That's how it works in Relativity. So, if you 'could' breach the speed of light, then you would be traveling backwards through time. However, Relativity doesn't explain how you would get back to your own time again.