Plasmonic nanoarrays which support collective surface lattice resonances (SLRs) have become an exciting frontier in plasmonics. Compared with the localized surface-plasmon resonance in individual particles, these collective modes have appealing advantages such as angle-dependent dispersions and much narrower linewidths. Here, we investigate systematically how the geometry of the lattice affects the SLRs supported by metallic nanoparticles. We present a general theoretical framework from which the various SLR modes of a given geometry can be straightforwardly obtained by a simple comparison of the diffractive order vectors and orientation of the nanoparticle dipole given by the polarization of the incident field. Our experimental measurements show that while square, rectangular, hexagonal, honeycomb, and Lieb lattice arrays have similar spectra near the Γ point (k=0), they have remarkably different SLR dispersions. Furthermore, their dispersions are highly dependent on the polarization. Numerical simulations are performed to elucidate the field profiles of the different modes. Our findings extend the diversity of SLRs in plasmonic nanoparticle arrays, and the theoretical framework provides a simple model for interpreting the SLRs features, and vice versa, for designing the geometrical patterns.