Mark Jacobson is a researcher at Stanford who sought to answer just that question. In his extensive analysis, he shows that the world’s energy can be produced through renewable sources including taking into account land base necessary for energy production.
Dr. Jacobson serves on the Department of Energy’s Energy Efficiency and Renewable Energy Advisory committee and you can learn more about that group here: http://www1.eere.energy.gov/eere_advisory_committee/
Learn more about Dr. Jacobson’s background here: http://www.stanford.edu/group/efmh/jacobson/
And read the first paper in the series here: http://www.stanford.edu/group/efmh/jacobson/Articles/I/JDEnPolicyPt1.pdf