  We investigate the gravitational memory effect for linearized perturbations
off of Minkowski space in odd spacetime dimensions $d$ by examining the effects
of gravitational radiation from classical point particle scattering. We also
investigate analogous memory effects for electromagnetic and scalar radiation.
We find that there is no gravitational memory effect in all odd dimensions. For
scalar and electromagnetic fields, there is no memory effect for $d\geq 7$; for
$d=3$ there is an infinite momentum memory effect, whereas for $d=5$ there is
no momentum memory effect but the displacement of a test particle will grow
unboundedly with time. Our results are further elucidated by analyzing the
memory effect for any slowly moving source of compact spatial support in odd
dimensions.
