  Using numerical simulations, we investigate vortex configurations and pinning
in superconductors with honeycomb and kagome pinning arrays. We find that a
variety of novel vortex crystal states can be stabilized at integer and
fractional matching field densities. The honeycomb and kagome pinning arrays
produce considerably more pronounced commensuration peaks in the critical
depinning force than triangular pinning arrays, and also cause additional peaks
at noninteger matching fields where a portion of the vortices are located in
the large interstitial regions of the pinning lattices. For the honeycomb
pinning array, we find matching effects of equal strength at most fillings
B/B_\phi=n/2 for n>2, where n is an integer, in agreement with recent
experiments. For kagome pinning arrays, pronounced matching effects generally
occur at B/B_\phi=n/3 for n>3, while for triangular pinning arrays pronounced
matching effects are observed only at integer fillings B/B_\phi=n. At the
noninteger matching field peaks in the honeycomb and kagome pinning arrays, the
interstitial vortices are arranged in dimer, trimer, and higher order n-mer
states that have an overall orientational order. We call these n-mer states
"vortex molecular crystals" and "vortex plastic crystals" since they are
similar to the states recently observed in colloidal molecular crystal systems.
We argue that the vortex molecular crystals have properties in common with
certain spin systems such as Ising and n-state Potts models. We show that
kagome and honeycomb pinning arrays can be useful for increasing the critical
current above that of purely triangular pinning arrays.
