  To elucidate the origin of spin structure-driven anomalous Hall effect (AHE)
in pyrochlore compounds, we construct the $t_{2g}$-orbital kagome lattice model
and analyze the anomalous Hall conductivity (AHC). We reveal that a conduction
electron acquires a Berry phase due to the complex d-orbital wavefunction in
the presence of spin-orbit interaction. This ``orbital Aharonov-Bohm (AB)
effect'' produces the AHC that is drastically changed in the presence of
non-collinear spin structure. In both ferromagnetic compound Nd$_2$Mo$_2$O$_7$
and paramagnetic compound Pr$_2$Ir$_2$O$_7$, the AHC given by the orbital AB
effect totally dominates the spin chirality mechanism, and succeeds in
explaining the experimental relation between the spin structure and the AHC.
Especially, ``finite AHC in the absence of magnetization'' observed in
Pr$_2$Ir$_2$O$_7$ can be explained in terms of the orbital mechanism by
assuming small magnetic order of Ir 5d-electrons.
