In a recent (July 2010) paper at arXiv.org, Seth Lloyd of the Massachusetts Institute of Technology notes that fiction has been grappling with these problems for far longer than science, but that even most fictional accounts, going at least as far back as the Mahabarata epic of ancient India, deal with travel into the future. "Perhaps because of the various paradoxes to which it gives rise, the concept of travel to the past is a more recent invention," says Lloyd, pointing to Charles Dickens' A Christmas Carol and Mark Twain's A Connecticut Yankee in King Arthur's Court. "The contemporary notion of time travel, together with all its attendant paradoxes, did not come into being until H.G. Wells masterpiece The Time Machine, which is also the first book to propose an actual device that can be used to travel back and forward in time."
To get around the grandfather paradox Lloyd and his co-authors suggest quantum teleportation and strict "post-selection" of what a time traveler could and could not do -- i.e. Read the rest