  The anomalous Hall effect (AHE) of epitaxial SrRuO$_3$ films with varying
lattice parameters is investigated, and analyzed according to the Berry-phase
scenario. SrRuO$_3$ thin films were deposited on SrTiO$_3$ substrates directly,
or using intermediate buffer layers, in order to finely control the epitaxial
strain. The AHE of the different films exhibits intrinsic features such as the
sign change of the Hall resistivity with the temperature, even for small
thicknesses of SrRuO$_3$. However, the anomalous Hall conductivity is greatly
reduced from its intrinsic value as the carrier scattering is increased when
the epitaxial strain is released. We argue that the AHE of fully strained
SrRuO$_3$ film with low residual resistivity represents the intrinsic AHE of
SrRuO$_3$.
