The long answer is also no! Moving clocks run slow — but always relative to another ‘stationary’ observer. In your own frame, you’ll live the same length of time you were always going to. However, it IS possible to ‘live longer’ compared to another, stationary population — but this is just another statement of what I wrote previously, namely moving clocks running slow.
The standard way the answer’s put is like this: imagine two twins, born on a planet. One twin hops in a spacecraft, goes away from the planet close to the speed of light for a while, turns around and comes back. He returns to find that his sibling is a lot older than he is. For a detailed description, have a look at http://en.wikipedia.org/wiki/Twin_paradox.