The technology might become feasible for a human mind to be "uploaded" to a computer where it could be backed up near-infinitely. A workshop was held in 2007 to survey the state of the art of the required technology, and the advances required to make it feasible. The research report was fascinating, but spoiler: it doesn't look like it'll be feasible until 50 or more years out.
Whole Brain Emulation: A RoadmapWhole brain emulation (WBE) is the possible future one-to-one modelling of the function of the human brain. It represents a formidable engineering and research problem, yet one which appears to have a well-defined goal and could, it would seem, be achieved by extrapolations of current technology.Since the implications of successful WBE are potentially very large the Future of Humanity Institute hosted a workshop in Oxford on 26-27 May, 2007. Invited experts from areas such as computational neuroscience, brain-scanning technology, computing, and neurobiology presented their findings and discussed the possibilities, problems and milestones that would have to be reached before WBE becomes feasible.