  Using the brick wall regularization of 't Hooft, the entropy of non-extreme
and extreme black holes is investigated in a general static, spherically
symmetric spacetime. We classify the singularity in the entropy by introducing
a {\it new} index $\delta $ with respect to the brick wall cut-off $\epsilon $.
The leading contribution to entropy for non-extreme case $(\delta \neq 0)$ is
shown to satisfy the area law with quadratic divergence with respect to the
invariant cut-off $\epsilon_{{\rm inv}}$ while the extreme case $(\delta =0)$
exhibits logarithmic divergence or constant value with respect to $\epsilon $.
The general formula is applied to Reissner-Nordstr\"{o}m, dilaton and
brane-world black holes and we obtain consistent results.
