  We show that dipolar interactions have dramatic effects on the groundstates
of rotating atomic Bose gases in the weak interaction limit. With increasing
dipolar interaction (relative to the net contact interaction), the mean-field,
or high filling fraction, groundstate undergoes a series of transitions between
vortex lattices of different symmetries: triangular, square, ``stripe'', and
``bubble'' phases. We also study the effects of dipolar interactions on the
quantum fluids at low filling fractions. We show that the incompressible
Laughlin state at filling fraction $\nu=1/2$ is replaced by compressible stripe
and bubble phases.
