We explore leptogenesis induced by the propagation of neutrinos in gravitational backgrounds that may occur in string theory. The first background is due to linear dilatons and the associated Kalb-Ramond field (axion) in four non-compact space-time dimensions of the string, and can be described within the framework of local effective lagrangians. The axion is linear in the time coordinate of the Einstein frame and gives rise to a constant torsion which couples to the fermion spin through a gravitational covariant derivative. This leads to different energy-momentum dispersion relations for fermions and anti-fermions and hence leptogenesis. The next two backgrounds go beyond the local effective lagrangian framework. One is a stochastic (Lorentz Violating) Finsler metric which again leads to different dispersion relations between fermions and antifermions. The third background of primary interest is the one due to populations of stochastically fluctuating point-like space-time defects that can be encountered in string/brane theory (D0 branes). Only neutral matter interacts non-trivially with these defects, as a consequence of charge conservation. Hence, such a background singles out neutrinos among the Standard Model excitations as the ones interacting predominantly with the defects. The back-reaction of the defects on the space-time due to their interaction with neutral matter results in stochastic Finsler-like metrics (similar to our second background). On average, the stochastic fluctuations of the D0 brane defects preserve Lorentz symmetry, but their variance is non-zero. Interestingly, the particle/antiparticle asymmetry comes out naturally to favour matter over antimatter in this third background, once the effects of the kinematics of the scattering of the D branes with matter is incorporated.