  We use a combination of numeric and analytic techniques to determine the
groun d state phase diagram of the Bose--Hubbard Hamiltonian with longer range
repulsi ve interactions. At half filling one finds superfluidity and an
insulating solid phase. Depending on the relative sizes of near--neighbor and
next near--neighbor interactions, this solid either follows a checkerboard or a
striped pattern. In neither case is there a coexistence with superfluidity.
However upon doping ``supersolid'' phases appear with simultaneous diagonal and
off--diagonal long range order.
