In this talk I want to describe recent work on geometric (Berry) phases that arise in the quantum theory of certain D-brane states. After briefly reviewing the geometric phase in general theories, I will turn to supersymmetric systems of the type arising in D0-brane configurations in string theory. Interestingly, the resulting Berry phases are related to the four Hopf fibrations. I will show how this fact arises as a consequence of the close relationship between SUSY and the division algebras. The framework of string theory allows to draw some interesting physical consequences from these Berry phases, such as a new interpretation of the Berry phase in terms of gravitational precession and the surprising result that in certain configurations, D0 branes behave as anyons.