  We present comparatively simple two-dimensional and three-dimensional
checkerboard-like optical lattices possessing nontrivial topological
properties. By simple tuning of the parameters these lattices can have a
topological insulating phase, a topological semi-metallic phase, or a trivial
insulating phase. This allows study of different topological phase transitions
within a single cold atom system. In the topologically nontrivial phases flat
bands appear at the surfaces of the system. These surface states possess short
localization lengths such that they are observable even in systems with small
lattice dimensions. Our proposed lattices neither need spin-orbit coupling nor
non-Abelian gauge fields to reach topologically nontrivial states.
