  We construct, using the supersymplectic framework of Berezin, Kostant and
others, two types of supersymmetric extensions of the Schr\"odinger algebra
(itself a conformal extension of the Galilei algebra). An `$I$-type' extension
exists in any space dimension, and for any pair of integers $N_+$ and $N_-$. It
yields an $N=N_++N_-$ superalgebra, which generalizes the N=1 supersymmetry
Gauntlett et al. found for a free spin-$\half$ particle, as well as the N=2
supersymmetry of the fermionic oscillator found by Beckers et al. In two space
dimensions, new, `exotic' or `$IJ$-type' extensions arise for each pair of
integers $\nu_+$ and $\nu_-$, yielding an $N=2(\nu_++\nu_-)$ superalgebra of
the type discovered recently by Leblanc et al. in non relativistic Chern-Simons
theory. For the magnetic monopole the symmetry reduces to
$\o(3)\times\osp(1/1)$, and for the magnetic vortex it reduces to
$\o(2)\times\osp(1/2)$.
