  We consider bosonic dipolar molecules in an optical lattice prepared in a
mixture of different rotational states. The 1/r^3 interaction between molecules
for this system is produced by exchanging a quantum of angular momentum between
two molecules. We show that the Mott states of such systems have a large
variety of non-trivial spin orderings including a state with ordering wave
vector that can be changed by tilting the lattice. As the Mott insulating phase
is melted, we also describe several exotic superfluid phases that will occur.
