  We explore several consequences of the recently discovered intrinsic
non-commutativity of the zero-mode sector of closed string theory. In
particular, we illuminate the relation between T-duality and this intrinsic
non-commutativity and also note that there is a simple closed string product,
equivalent to the splitting-joining interaction of the pants diagram, that
respects this non-commutativity and is covariant with respect to T-duality. We
emphasize the central role played by the symplectic form $\omega$ on the space
of zero modes. Furthermore, we begin an exploration of new non-commutative
string backgrounds. In particular, we show that a constant non-geometric
background field leads to a non-commutative space-time. We also comment on the
non-associativity that consequently arises in the presence of non-trivial flux.
In this formulation, the $H$-flux as well as the `non-geometric' $Q$-, $R$- and
$F$-fluxes are simply the various components of the flux of an almost
symplectic form.
