  Itinerant electrons in a two-dimensional Kagome lattice form a Dirac
semi-metal, similar to graphene. When lattice and spin symmetries are broken by
various periodic perturbations this semi-metal is shown to spawn interesting
non-magnetic insulating phases. These include a two-dimensional topological
insulator with a non-trivial Z_2 invariant and robust gapless edge states, as
well as dimerized and trimerized `Kekule' insulators. The latter two are
topologically trivial but the Kekule phase possesses a complex order parameter
with fractionally charged vortex excitations. A charge density wave is shown to
couple to the Dirac fermions as an effective axial gauge field.
