We investigate bosonic atoms or molecules interacting via dipolar interactions in a planar array of one-dimensional tubes. We consider the situation in which the dipoles are oriented perpendicular to the tubes by an external field. We find various quantum phases reaching from a “sliding Luttinger liquid” phase to a two-dimensional charge density wave ordered phase. Two different kinds of charge density wave order occur: a stripe phase in which the bosons in different tubes are aligned and a checkerboard phase. We further point out how to distinguish the occurring phases experimentally.