  We use the Bogoliubov-de Gennes formalism and study the ground-state phases
of trapped spin-orbit coupled Fermi gases in two dimensions. Our main finding
is that the presence of a symmetric (Rashba type) spin-orbit coupling
spontaneously induces counterflowing mass currents in the vicinity of the trap
edge, i.e. $\uparrow$ and $\downarrow$ particles circulate in opposite
directions with equal speed. These currents flow even in noninteracting
systems, but their strength decreases toward the molecular BEC limit, which can
be achieved either by increasing the spin-orbit coupling or the interaction
strength. These currents are also quite robust against the effects of
asymmetric spin-orbit couplings in $x$ and $y$ directions, gradually reducing
to zero as the spin-orbit coupling becomes one dimensional. We compare our
results with those of chiral p-wave superfluids/superconductors.
