  We investigate the general structure of orbital exchange physics in
Mott-insulating states of $p$-orbital systems in optical lattices. Orbital
orders occur in both the triangular and Kagome lattices. In contrast, orbital
exchange in the honeycomb lattice is frustrated as described by a novel quantum
120$^\circ$-model. Its classical ground states are mapped into configurations
of the fully-packed loop model with an extra U(1) rotation degree of freedom.
Quantum orbital fluctuations select a six-site plaquette ground state ordering
pattern in the semiclassical limit from the ``order from disorder'' mechanism.
This effect arises from the appearance of a zero energy flat-band of orbital
excitations.
